This is a Makkan verse (Tafsir Ibn kathir). Fighting was only legislated when the Muslims were exiled out of Makkah to Madinah. However, there other scholars who are of the opinion that it was revealed in Madinah (Mawdudi and Abdullah Yusuf Ali).
“Indeed, your Lord knows, [O Muhammad], that you stand [in prayer] almost two thirds of the night or half of it or a third of it, and [so do] a group of those with you. And Allah determines [the extent of] the night and the day. He has known that you [Muslims] will not be able to do it and has turned to you in forgiveness, so recite what is easy [for you] of the Qur’an. He has known that there will be among you those who are ill and others traveling throughout the land seeking [something] of the bounty of Allah and others fighting for the cause of Allah. So recite what is easy from it and establish prayer and give zakah and loan Allah a goodly loan. And whatever good you put forward for yourselves – you will find it with Allah. It is better and greater in reward. And seek forgiveness of Allah. Indeed, Allah is Forgiving and Merciful.” – Quran 73:20
“Fighting for the cause of God”, was done in life-time of Prophet Muhammed (p) as a result of the continued oppression and persecution the Muslims faced. Prophet Muhammed’s (p) principle was to fight those who persecute and oppress people:
“O God! Let us enjoy our hearing, our sight and our power as long as you keep us alive and make our heirs from our own offspring, and make our revenge RESTRICTED TO THOSE WHO OPPRESS US, and support us AGAINST THOSE WHO ARE HOSTILE TO US let no misfortune afflict our Deen: let not worldly affairs be our principal concern, or the ultimate limit of our knowledge, and let not those rule over us who do not show mercy to us.” (Riyad as-Salihin Book 5. Hadith 834)
The Prophet never initiated attacks against anyone unless they took up arms against him or his people first.
Tafsir Ibn Kathir:
(He knows that there will be some among you sick, others traveling through the land, seeking of Allah’s bounty, yet others fighting in Allah’s cause.) meaning, He knows that there will be people of this nation who will have excuses for not praying the (voluntary) night prayer. They are those who are ill and therefore they are not able to perform it, and those who are traveling in the land seeking the bounty of Allah in business and trade, and others who will be busy with that which is more important to them. An example of this is going on expeditions to fight in the way of Allah. This Ayah, rather, this entire Surah was revealed in Makkah even though fighting was not legislated until after it was revealed. Thus, it is among the greatest of the signs of Prophethood, because it informs about unseen matters of the future. …” (Tafsir Ibn Kathir on Surah 73:20 – Online Source)
Malik Ghulam Farid:
“3157. In the opening verse of the Surah the Holy Prophet was enjoined constantly to pray at night, for, that would give him the necessary strength to discharge the grave responsibility of preaching the Divine Message that was shortly going to devolve on him. In this verse he is assured of Divine pleasure, and is told that he has faithfully carried out God’s command about Night prayer – not only he, but a party of believers also. The command was not specifically directed to the followers of the Holy Prophet, but being always desirous of the following in his footsteps, they copied his example in this respect also.
3158. The sentence, ‘Allah determines the measure of the night and the day,’ signifies that sometimes nights are long and sometimes they are short and sometimes they are equal. The words, ‘you cannot calculate the time accurately,’ may apply to Muslims in general. They are told that all of them would not be able to say the Night-prayer regularly and punctually.” 
Maulana Muhammad Ali:
“20a. The first portion of the verse simply states the fact that the Holy Prophet and those with him passed sometimes two-thirds, sometimes a half, and sometimes a third of the night in prayer; and hence it is meaningless to say that the first portion of the verse is abrogated by the second. The latter portion of the verse states that, though the Holy Prophet and his early zealous companions passed a great part of the night in prayer, all Muslims could not follow their example, and hence they are told that they might pray by night so long as it was easy to them and not a burden. By the reading of the Qur’an is here meant its recital in the night-prayer called tahajjud.
20b. The mention here of fighting is very probably a prophetical statement, as we find in many other places in the Holy Qur’an; hence the occurrence of the word is no argument that the verse was not revealed at Makkah.” 
Dr. Muhammad Asad:
“11 Lit., “of those who are with thee”. With this concluding passage, the discourse returns to the theme of the opening verses, namely, the great spiritual value of praying at night.
12 Lit., “count it”, i.e., the length of your vigil.
13 This reference to “fighting in God’s cause” has induced many commentators to assume that the whole of verse 20 was revealed at Medina; that is, years after the rest of the surah: for, the principle of “fighting in God’s cause” (jihad) was introduced only after the Prophet’s hijrah from Mecca to Medina. This assumption must, however, be dismissed as unwarranted. Although there is no doubt that jihad was first sanctioned during the Medina period, the sentence in question is clearly expressed in the future tense: “in time there will be” (sayakun) – and must, therefore, as Ibn Kathir points out, be understood as a prediction of future circumstances. With all this, the above passage stresses the necessity of avoiding all exaggeration even in one’s devotions.
14 For an explanation of the term zakah – of which the above is the earliest Qur’anic instance – see surah 2, note 34.” 
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 The Holy Qur’an – Arabic Text With English Translation & Short Commentary By Malik Ghulam Farid, Page 1194
 The Holy Quran Arabic Text with English Translation, Commentary and comprehensive Introduction by Maulana Muhammad Ali, Page 1148
 The Message of The Quran translated and explained by Dr. Muhammad Asad, page 1220 – 1221