Sun tan lotion can soften or dissolve your acrylic nails or nail polish according to this article on Beauty Brains.

If you want to find out if your sun tan lotion of choice will ruin your nails, try this (from Beauty Brain):

Smear a little of your favourite nail polish on a piece of glass (you can use an empty nail polish bottle or even a old compact mirror. Then, take that with you when you’re shopping for a sunscreen. Squeeze a little of the sunscreen product onto your polish smear and see if it softens the film. That should be a pretty good indicator if it will be okay when you actually apply it with your manicured fingers.

They also refer to another article worth reading: 3 Ways to Tell if Your Sunscreen is Bad.