Is there a way to tell if software on that runs on one version of OS X will run on another version of OS X without install the new version of OS X, and then attempting to reinstall the software?
Short anser, no. The long answer is there are a few general rules with mac software support. If an app is built for PowerPC, it will only work up to 10.6 Snow Leopard as Lion dropped PowerPC support. Anything built for Intel macs should work with 10.5+.
Apps available on the App Store will say what their hardware requirements, and I believe all should work on lion.