If someone trespasses on a private beach and drowns swimming in the lake, is the owner of the property liable, even if signs are posted saying "Private Beach" and "No swimming when lifeguard not present?"?

I live in NY State in a complex that has a beach owned by the homeowner’s association. The whole complex has signs saying “Private” and the beach has signs saying “Private Beach.” There are also signs posted at the beach that say “No swimming when lifeguard not on duty” and has the hours that the lifeguards are on duty.

If someone comes and trespasses and goes swimming when the lifeguards are not on duty, and they drown, is the homeowner’s association liable, even though the people trespass and even though they swam when no lifeguard was on duty?

Again, I live in NY state.

I ask because there was a family swimming before, and I told them that the beach is for people who live here. I want to write a letter to the homeowners’ association about more people coming here who don’t live here, and I want to reference liability, but only if it’s correct that it would be a liability despite the signs.