I have a Lefty on an older Cannondale Jekyll... not an imressive fork, and certainly not something I would even consider using as a "pit" bike. On the plus side, it has a remote lock-out, which I would use.. essentially eliminating the whole purpose other than adding weight to the front of the bike
There is an adapter kit by a company called Project 321 (or something like that) to fit Leftys on a 1 1/8" steer tube. With that said, putting a suspension fork of any kind will likely jack up the geometry of a 'cross bike. Most 'cross bikes will have an Axle-Crown measurement in the range of 395mm and an 80mm travel mountain bike fork will have an A-C in the range of 450mm. That means you will raise the front end of your bike up 2+ inches!
Aside from messing up the geometry of your bike the cost of a Lefty + steer tube adapter + new front wheel + disc brake = the cost of just buying a nice entry level mountain bike.
I'd save the cash and just buy a new bike. Nothing wrong with having a bike for every purpose!