Can a Kenmore 158.13360 sew leather?

Yes, if the leather is thin enough, your needle sharp enough, and thread strong enough. Look for a thin, soft leather such as kid. It will help to change out your needle to a much sharper "leather" needle, which also has more metal between the tip and the eye, to punch through the heavy material better before pulling thread through it. You may want to use nylon filament as replacement for normal thread. You won't hurt any part of the machine proper, but be careful you don't push the motor too hard; you don't want to burn it out or break the belt.

You may have to adjust the thread tensions, since the top thread will be pulling through thick material. Don't expect to sew quickly. Although your machine (a model 33) is a workhorse, leather is usually sewn on specialized machines, and you are asking it to do something a bit out of its league.