If I upgrade to OS X 10.7 (Lion), will Intuit Quicken still work?
Unfortunately, no.  Quicken 2007 requires Rosetta which Apple has decided to leave behind in their OS.  MacWorld.com has a great article here with some great alternatives, but right now, you need to either give up Quicken 2007, or wait on Lion until you are ready to do so.

Dual booting is also possible, but it's not a convenient solution to just run banking software.