Is merely desiring the act of the people of Lut, and sufficing with that, without performing the act, considered sodomy, and does it carry the same ruling?

Congratulations on your repentance. Masturbation and sodomy are forbidden. Merely thinking about sin is not punishable, for the Prophet, peace and blessings be upon him, said: "Indeed, Allah has forgiven my nation for what their hearts whisper, as long as they do not act upon it or speak of it." What occurred is not considered sodomy unless it was acted upon or spoken of.