Final Cut Pro 5.1 will run, as it is a Universal Binary, but as far as I can remember, the installer is still PPC only, thus it won't start on Lion, for that Snow Leopard is needed (which can still be installed upon a 2011 iMac, that came with Lion).
What do you mean with that exactly?
If the applications you use are Universal Binary*, then they will run in Lion, Intel applications too, but PPC applications can only be run in pre-Lion Mac OS X versions.