Like said, it MAY work, but it may also not work. Apple's upgrade system is really only designed to work with the previous version, so when you try and upgrade from two or more versions back, the results are unpredictable. Sometimes it works without a hitch, sometimes it just makes a mess of things.
Now, one minor detail, since you're running an OS version which leaves at least some degree of ambiguity. If you have a PowerPC based system (G4 or G5), then 10.6 or later will not run on your system. For 10.7 you need a system with at least a Core 2 Duo (a Core Duo won't cut it). You don't give any details on the system you're using, so if you go to the Apple icon in the menu bar, select About This Mac, and you don't see Core 2 Duo or Xeon next to where it says Processor, then 10.7 will not run on your system. A Core i3/i5/i7 would also work, but if you had a unit with one of those CPUs, it would already be running 10.6 or 10.7.