“We don’t have a formal policy, but we can’t commit to providing a female lifeguard because it would run against the establishment clause of providing a service on the basis of a religious belief,” Liam Kavanagh, first deputy commissioner for parks and recreation, said of the Hasidic request.
Sounds like gobbeldygook to me. It seems to makes sense that women who want to go to a pool without men wouldn't want a male lifeguard (though are some who would permit it from a halachic point of view).
Rav Aviner allowed a leniency, though the assumption here is that there is a shortage of female lifeguards, something that I doubt exists in NYC. On the Air with Ha-Rav Shlomo Aviner