+1 for Jerry’s Color suggestion. It’s the proper tool for the job. It’s a bit weak for a few things, but it’s built for video and it’s incredibly powerful.
The major downfall with using Lightroom would be the inability to change the effect over time apart from frame-by-frame dialing in the changes you want.
If you really want to put a square peg in a round hole you could export your project as an image sequence and import thousands of frames into Lightroom. You would find your develop settings on the first clip and paste paste them to the rest of the images in that clip. After getting all your develop settings down export out of Lightroom as TIFs with the same file names but in a different folder and open in Quicktime as an image sequence. Save/Export the Image Sequence as a QT movie, bring it back into Final Cut and merge your audio in, and there you go.
Naturally using this many TIF files will take a toll on your hard drive, so make sure you have a lot of space before you get started.