I’ve noticed that in several older video games (mostly on NES) that the word "rest" is used to indicate the number of lives you have left.

For example, the screen before a level starts would say something like:

Stage 3

Rest 5

Why is this?

I’d personally guess that it was a matter of translation. Rest could have been "reset" and many of the meanings of life/lives are similar enough to rest to interchange them in a translation. There are a lot of translation blunders from that era of gaming.