Four New Yorkers who live in shelters or are at risk of homelessness sued Mayor Eric Adams and his administration on Wednesday for refusing to implement new laws that’d make it easier for them to access the city’s rental assistance program. The shelter residents, joined by lawyers from the Legal Aid Society and members of the City Council, were expected to discuss the rare legal action against the mayor during a morning press conference on the steps of City Hall. The suit filed in Manhattan Supreme Court by the quartet — Marie Vincent, Carolina Tejeda, Mary Cronneit and Susan Acks — asks a jud…