When the shows let out, it is not considered late night. You will surprised at the amount of activity at the confluence of Broadway and 9th Ave. You might have trouble getting a cab, not because of scarcity but because of competition.

Other options include the "1" train dirrectly under Lincoln Center and the 5, 7, 11, 0r 104 buses depending where on 41 st your hotel is located.

http://www.mta.info/

New York city is really still alive and bustling even on what you call late night

11 pm is NOT late in NYC. Late night transport would be considered 3 or 4 am. Subway and buses run 24/7 - although not every 5 minutes as they do during the day. At 11 pm they might be every 2 to 15 minutes.

Taking either the bus or subway would be perfectly safe although you may have to wait a few minutes. Getting a cab will be very difficult.

If it were me I would walk back to the hotel - since a nice stroll after sitting for so long is likely to make it easier to get to sleep.

As Aduchamp1 has mentioned, cabs are hard to come by at that hour in that location, but the convenient subways and buses are not!

For guaranteed transport, you can book a car service like
allstatelimo.com
dial7.com
but they'll charge a fortune for the privilege. You don't say where on 41 st. (every location in NYC must have at least 2 cross streets to identify the location) but assuming it's on the west side, you could take the bus down Broadway to 41 st. if you don't want to use the subway.

If you have mobility issues, buses are a great way to get around NYC. All the buses are kneeling buses so the steps lower to meet you at street level and then you can easily climb on the bus.
I highly recommend the bus. It may take little longer than the subway but at 11 pm the subways aren't running as frequently either. The bus is also great because you are perched just high enough above the rest of the traffic to be able to watch out the windows and see the city go by.

You can check out bus routes and schedules at the mta website and hopstop can also give you bus directions to your hotel. You should also know that you can request a transfer from a uptown/downtown bus to a crosstown bus within 2 hours, or you can swipe your metrocard again and it should work as a transfer. so if you take the bus down broadway and need to go crosstown on 42nd, you should be able to do it on the same fare.

The problem with car services is that they charge for waiting time although I am sure Lincoln center can provide a good guess as to the time of the final curtain.