My wife and I will be arriving Munich from Rome on LH with a First Class boarding pass on to Chicago. Actual time from scheduled arrival to departure is 1 hour 50 minutes. What is the lounge situation there. Anything special to do or see at the airport?

You have a few options. There are two SEN/*G lounges on the schengen level with standard SEN lounge ammenities: showers/beer/good food/internet terminals, one opposite G24 (larger) and another opposite G28 (smaller), quite close to each-other.
On the non-schengen level there's a lounge opposite H24. I've never been to this one so I can't comment, but I'm sure it's like the other ones, since all of LH lounges are pretty much the same.

When you land, you'll be on the Schengen level, so you'll have an option to visit all 3 lounges .

There's a beer garden between T1 and T2, but I wouldn't go out, as LH has MUC beer inside the lounges on tap.

The train into town takes 45 mins each way, so that's out of the question for you.

Here is LH's description of First Class services at MUC

If it's on LH, you will probably have access to the FCL, which would be the absolute MUST!



Of the Senaor Lounges, I prefer the Schengen ones.

There Biergarten is actually quite nice and a typical Bavarian experience (to the extent possible) so, if you haven't been to a German Biergarten yet, I would consider that even though the FCL is very nice.

If the OP is indeed flying on LH F to ORD, a visit to the FCL is recommended. Arriving from ROM you can enter the FCL on Level G (Schengen), go upstairs to the integrated passport control within the lounge and exit on Level H (non-Schengen). The most civilised passport control I've come across (although as you are leaving Schengen there isn't much formality anyway).

Here are some photos of the Munich FCL on flickr.

Anotehr vote for FCL .... if on LH!