Boot off of an external hard drive I made 2 partitions on my external hard drive. One is 240ish GB and one is 10GB. I put the OS X Lion install image on the 10GB partition (using restore) and when that finished I tried to boot from that hard drive but it doesn't show up, just my regular hard drive that is in my computer.

I am on a mid-2012 MacBook Pro running macOS Sierra
It's probably the lion image. try a different image. Try to google : "index of" Install OS X Lion

then click on some of the links and once the dmg download is complete get the installesd.dmg from the image and burn it using disk utility