Whoever disbelieves in Allah after his belief… except for one who is forced [to renounce his religion] while his heart is secure in faith. But those who [willingly] open their breasts to disbelief, upon them is wrath from Allah, and for them is a great punishment. Quran 16:106
The above verse has been used by critics that Muslims are allowed to lie in all circumstances. Before we move forward on whether the verse gives approval of such, let’s first look at the verses in its historical context, why it was revealed.
The early Muslim community suffered many persecutions at the hands of disbelievers in Makkah. Those who did not have strong ties with family were more vulnerable to get tortured by the disbelievers. In many of these instances, many Muslims lost their lives for believing in One God and His final Messenger i.e., Islam.
The verse under discussion was revealed because some Muslims (Companions of Prophet Muhammad (p)) were tortured and uttered disbelief so that the persecutors stopped tormenting them. Although they uttered the words, they still believed in Islam, and merely said it so the persecution stops. Hence, the Quran states that those who had done such, there is no blame on them for what they did, and said these things when they were in a situation where it meant either to live and continually be under torture or be put to death. So, there was no sin on those who said things which were contrary to what they believed in their heart.
Moreover, the claim by critics that the verse sanctions Muslims to lie to disbelievers in ‘all circumstances’ is false. All commentaries agree that only in such situations were one is tortured is one allowed to say things which are not true.
Quran Commentaries on Quran 16:106
Illuminating Discourses on the Noble Quran – Tafseer Anwarul Bayan – Shaykh Ashiq Ilahi Madni
Sayyidina Abdullah bin Mas’ud mentions further that all of them besides Bilal uttered such words such words to save themselves. Bilal was prepared to sacrifice his life for Allah and was constantly tortured until Abu Bakr bought his freedom. Sumayya was privileged enough to be the first person to be martyred in the history of Islam [Al Bidaya wan Nihayah v.3 p.55 59]. The above verse was revealed with regard to the other Sahabah who were forced by the polytheists to otter words of infidelity (kufr). Although they said these words, they still remained staunch believers. Durrul Manthur (v.3 p. 132) reports that the polytheists once apprehended Ammar bin Yasir and only left him when he spoke ill of the Holy Prophet and praised their idols. He later came to the Holy Prophet, who asked him how things were. He replied that matters were exceptionally unfavourable. Thereafter he told the Holy Prophet that he had lied when he spoke ill of the Holy Prophet and praised the idols. The Holy Prophet asked him what was the condition of his heart? He replied that it was content with belief (Iman). The Holy prophet told him that he could repeat those words if ever the disbelievers (Kuffar) were to harass him in that manner. On this occasion Allah revealed the verse, ‘save for him who is forced, but his heart is content with belief (Iman).’
Durrul Manthur reports that two Muslims were captured and brought before Musailama Kadhdhab. When he asked the one whether he attested to the Prophethood of Muhammad, he replied in the affirmative. When he asked him whether he (Musailama) was Allah’s prophet, the sahaba placed his fingers in his ears, denoting that he was deaf to the statement. Musailama then had him killed. Then turning his attention to the second Sah’abi, Musailama posed the same questions to him. He replied that he also believed to be Allah’s Prophet. Consequently, he was released. When he returned to the Holy prophet, he related the incident to him. The Holy Prophet said, ‘Your Companion has passed away with belief (Iman) and you have practitised the concession.’ It is learnt from this that mere verbal threats will not be regarded as ‘force’. … 
Ma’arifulul-Qur’an – Maulana Muhammad Shaffi
From the first verse (106) comes the religious ruling about a person who has been compelled to utter a word of infidelity (kufr) under the threat that he would be killed if he did not do that. If he feels that, in all likelihood, the people threatening him have full capability of doing just that, then, this is a state of duress. If he were to utter some word of disbelief verbally – but, with a heart firm on faith, a heart that shuns saying what is false and evil – then, there is no sin on him. …
This verse was revealed about the noble Sahabah who were arrested by the Mushriks. Their disbelieving captors had told them that they must return to infidelity failing which they would be killed.
The Message of The Quran – Muhammad Asad
133 Lit., ‘except’ – but the Arabic construction of the sentence that follows makes it necessary to render the simple particle ills in the manner adopted by me (‘and this, to be sure, does not apply to …, etc.).
134 Lit., ‘one who is coerced, the while his heart is at rest in [his] faith’. This relates to believers who under torture or threat of death, ostensibly ‘recant’ in order to save themselves. Although the Qur’an makes it clear in several places that martyrdom in the cause of faith is highly meritorious, ‘God does not burden any human being with more than he is well able to bear’ (Cf. 2:233 and 286, 6:152, 7:42, 23:62, and many other Qur’anic statements to the same effect). 
Sayyid Abul Ala Maududi – Tafhim al-Qur’an – The Meaning of the Qur’an
109 This verse deals with the case of those Muslims who were being persecuted with cruelty and were being-subjected to unbearable torments to force them to give up their Faith. They are being told that if at any time they are forced to utter words of disbelief to save their lives, when in fact in their hearts they are secure against disbelief, they will be pardoned. On the other hand, if they accepted unbelief from the core of their hearts, they shall not escape the torment of Allah even if they succeed in saving their lives.
It does not, however, mean that one should utter words of disbelief to save one’s life. This is merely a permission but not the ideal thing for a Believer. According to this permission if one utters such a thing, he shall not be taken to account. In fact, the ideal for a Believer is to utter words of truth in any case whether his body is cut into pieces. There are instances which show that during the period of the Holy Prophet some acted upon the ideal while others took advantage of the permission. There was Khabbab bin Art (May Allah be pleased with him) who was made to lie on embers of fire until the fire was extinguished by the melting of his fat, but he remained firm in his Faith. Then there was Bilal Habashi (May Allah be pleased with him) who was made to put on an armor and stand in the scorching heat. Then he was dragged on the burning sand but he went on saying, “Allah is one.” There was another Believer, Habib Gin Zaid bin `Asim, whose limbs were cut one by one by the order of Musailimah, the Liar. Each time his limb was severed it was demanded of him that he should acknowledge the Liar as a prophet but each time he refused to bear witness to his claim of prophethood until he breathed his last. On the other hand, there was the instance of Ammar bin Yasir (May Allah be pleased with him) whose parents were mercilessly butchered before his eyes. After this he himself was put to such unbearable torture that, in order to save his life, he had to utter the same words of unbelief that were demanded of him. Afterwards when he came crying to the Holy Prophet, he said, “O Messenger of Allah, they did not let me go until I spoke evil of you and praised their deities” . The Holy Prophet asked him, “How do you feel about this, in your heart?” He replied humbly, “My heart is fully convinced of the Faith.” At this the Holy Prophet replied, “If they put you to the same torture again, you may utter the same words”. 
Maulana Muhammad Ali
106a. Only very rare instances are met with in the early history of Islam in which the converts even under compulsion ever recanted. For instance, Yasir and Sumayyah, husband and wife, suffered death at the hands of the disbelievers because they would not recant, the latter being put to death most cruelly, her legs being tied to two camels which were made to run in opposite directions. Their son Ammar, however, was not so resolute. The cruellest persecutions were inflicted on those slaves who had become converts to Islam. Muir says: ‘These were seized and imprisoned, or they were exposed upon the scorching gravel of the valley to the intense glare of the midday sun. The torment was enhanced by intolerable thirst, until the wretched sufferers hardly knew what they said.’ Yet even under these trying circumstances, which would have maddened even the most resolute man, there were those among these slave-converts who were as firm as a mountain; as in the case of Bilal, of whom it is recorded that ‘ in the depth of his anguish the persecutors could force from him but on expression, Ahad! Ahad! (One! One! God)’ (Muir). 
 Illuminating Discourses on the Noble Quran – Tafseer Anwarul Bayan – By Shaykh Ashiq Ilahi Madni, volume 3, page 219 – 220
 Ma’arifulul-Qur’an By Maulana Muhammad Shaffi volume 5, page 417
 The Message of The Quran – translated and explained by Muhammad Asad page 589
 Sayyid Abul Ala Maududi – Tafhim al-Qur’an – The Meaning of the Qur’an
 The Holy Quran – Arabic Text with English Translation, Commentary and comprehensive Introduction [Year 2002 Edition] by Maulana Muhammad Ali, page 556