Q:

live as a noun?

They are living their lives to the full.
They are living full lives.
Updated: I am wondering if the two mean the same thing.

A:

The plural noun lives is written as life in the singular – much like knives is the plural of knife, and wives is the plural of wife. 
As for whether or not your two similar expressions mean the same thing, it's hard to tell what they even mean without context, really. The expression living life to the fullest is a fairly common idiom, but what it means is subject to interpretation. Take a fellow who get drunk with his friends four nights of the week. His partying friends might think he's “living life to the fullest,” but other acquaintances might regard him as an alcoholic who is squandering his talents and gifts. You can find out more about the expression here on ELL.
If w change the superlative fullest to full, and does the expression change in meaning? Maybe not too much – perhaps they are both ways of saying carpe diem. Then again, maybe a full life means something different altogether. For example, maybe a person with a “full life” is one who is just very busy with obligations:

Wanna go out for lunch next week?
I'd love to, but my schedule is packed. My life is so full right now.
  I know what you mean. It seems like I'm running on fumes every day, too.

It sounds like those two friends are living full lives, too, but in a very different way.

