So, LH is a great product, and they are flying more 747-8's which does have layflat business, but if you do LH, I'd recommend at least half the folks fly in F, so you get the First Class Lounge or Terminal.
Other options: There is a direct ORD-FCO on United, they fly a 3-cabin 772, both J and F have layflats, its my preferred J seat of UA (vs. pre-merger CO's seat which they have on the dreamliner that sucks!).
If you have the Alaska miles, you could try flying EK A380 via Dubai, that's a lot of fun, and last I checked Emirates does fly to Rome, that'd be 100k AS miles though, one way. You could even do a stopover in Dubai.
While its not spectacular, Finnair flies from I think ORD (I know they fly from JFK), and has a above average business class, from what I've read. They also have a sauna at the airport, which could be cool to do.
If there were a *reasonable* way to book Air France first class, I'd recommend considering that, as the lounge sounds to be great in CDG, although, you'd be spinning the roulette wheel of whether you'll encounter an ATC strike, pilot strike, ground crew strike, or flight attendant strike.