I've never seen aphids on Peace Lily (Spathiphyllum), but that doesn't mean they don't bother them. It is more likely gnats. They thrive in the same thing Spaths like, i.e. organic soil that is damp. This website explains them pretty well. Thanks to the Extension service from Colorado State.

http://www.ext.colostate.edu/pubs/insect/05584.html

Aphids are on growth tips, and crotches, not in the soil. They make the growth abnormal, flowers fail to open, you can see them on the plant. They can be different colors but are all about the same size, do the same thing.

Here is a link that might be useful: google images of aphids