I doubt it. It could be done, but you'd have to go out of your way to make it happen. You'd either have to partition your drive or use a secondary drive, probably external.
You can install a different OS onto a given partition, and then select that partition using the boot selector, same as a secondary or tertiary drive, but you'll be on your own to manage it all.
But I don't really understand the point in all of this. Virtually all software will continue working exactly the same as it has. The only exceptions would probably be very old software that are using now depreciated APIs. So that would mean that either the programs have been abandoned, or the developers are lazy (or possibly inept) and failed to act within the ample time (over a year) provided to them. Either scenario makes for a compelling case to find a replacement program.
I have two Macs that run Snow Leopard. Lion looks to be quite different and offer great new features, particularly the app store. So, can a Mac become dual boot like a Linux can? I mean, may I co-install Lion side by side with Snow leopard rather than overwrite it? I have successfully done this operation on a Linux Ubuntu netbook with two different versions of Ubuntu, and a Windows 7/Ubuntu netbook. But I've never tried this on a Mac. Does a Mac OSX install allow options for how the user will install the new OS?