Learn Russian: Два года назад мы жили здесь.

In Russian, the numbers 2, 3, and 4 are followed by a noun in the genitive singular. The genitive singular of год (year) is года. You only use лет (the genitive plural) for numbers 5 and above, or with quantity words like много (a lot).

I thought назад meant back. How does it mean ago here?

You are right that назад often means back as a direction. However, when you place it immediately after a measurement of time, like два года назад (literally two years back), it is the standard way to say ago in Russian.

Why do we use the imperfective verb жили instead of a perfective verb, since the living is in the past and finished?

Even though the action happened in the past and is over, living somewhere is a continuous state or process rather than a single completed, instantaneous event. For ongoing or continuous states in the past, Russian always uses the imperfective aspect, which gives us жили.

Is it okay to change the word order and say Мы жили здесь два года назад?

Yes, that is perfectly correct. Russian word order is flexible. Putting Два года назад at the very beginning of the sentence simply sets the time and scene first, which is a very natural and common way to start a thought in Russian.