Only a fool would try to predict what the Supreme Court will say, but here goes: I suspect the court will signal that either or both of two approaches is acceptable. A local government can authorize a chaplain to open its sessions, if it does not permit openly sectarian prayer; or it can invite a variety of speakers to pray, as Town of Greece did, without policing the content of the prayers, so long as it does not discriminate in its selection.
As an advocate of a strict “wall of separation,” Alton Lemon might chafe at this approach. But it would fit the Supreme Court’s gradual and welcome shift toward treating religion and nonreligion evenhandedly.