Went to Lyman's a few months ago and saw the same message in sharpie, made me chuckle. The hand drawn map wasn't there on my most recent visit, but even still I could immediately tell someone was just having fun trolling people. Tunnels under Lyman's is news to me, though not very surprising considering how large it must have been. The tunnels under the hospital are pretty extensive, and there are some passages that are still cinderblocked up, but I really doubt there is a tunnel from the hospital grounds to Lyman's, it would have to be at least a mile long, probably more.
https://flic.kr/p/FnYDTqUrbex challenge
https://flic.kr/p/FKN8o1Here's a shot of the tunnels under the hospital.
I want to go back to Lyman's again now.