I live in 3 story condominium in New York and the 3rd floor owner has water damage from the roof. He is getting that fixed and wants me to pay or put a lien on my 1st floor property.

How does he figure you are responsible?

Here is the NY title on liens. I don't see anything that appears to be applicable. Mechanic's Liens is the closest, probably.

Could be he is making empty threats, not really knowing what he's talking about. But again, how does he figure a 1st floor owner is responsible for roof leakage affecting the third floor?

If this is a condo, then each condo owner has responsibility for common areas. The roof could be considered a common area. Therefore all owners in the building might be assessed a share of the cost of repairing the roof.

However, the owner of the 3rd floor condo can't do this on his own. This has to be done by the HOA or other entity that represent the corporation.

I think more details are needed here to properly advise.