Well, besides finding the key, the villager will reward you as well. Sometimes an item, and sometimes with bells. I got 650 bells for rescuing Gala's key last time. Also, I've found that some villagers are more prone to lose their keys than others. As long as you get it the same day they lose the key, you'll get a reward and I think it also raises your friendship level with that villager. If you can't find it, and it's pretty easy, just look for the smaller fish, not the tiny one though. You'll probably get a few fish first. If they live in the lower part of town, their key usually can be found in the lower river, and if they live above, the upper river is a good bet for them.
Once in a great while I'll have to try the opposite, but usually this holds true. Sometimes I find it right away, and sometimes I have to catch a few fish before it shows up.
GG loves ACNH!