Churches are private property because they are not owned by the govenment, but members of the public walk into churches worldwide, every single day. AFAIK, the Cities Church does not have a "No Trespassing" or "Private Property" sign (although we know churches ARE privately owned). A church is not normally closed to members of the public, of which the group, including Lemon, were members of the public.
IMO, as far as trespassing, if there was no signage and the door was open to members of the public, it then becomes trespassing only when/if they are asked to leave and do not do so. Someone would have to determine a legally required length of time in which they were required to leave before it constitutes trespassing.
IMO