Elves and Dwarves are already classed as immortals, but the old school D&D concept of immortals as characters who have transcended levels is also a setting fact. The Mesopotamian pantheon accounts for roughly 2,000 gods; there are also regional “Champions of Law” roughly equivalent to Christian Saints (which is also roughly equivalent to the level of power that the Powers of Neutrality / the Celtic Pantheon possess). Humans generally start to become eligible after they hit 26th level.
Alexander of Macedonia became an immortal, but most of the press is reserved for members of the Imperial royal family that do. Yes, as with Clerics, you also have to be Aligned “with Law” to be eligible. Neutrality generally does not grant an equivalent option to humans; and Chaos, as with many things, has its own perverse interpretation.