Both Uses of

immortal
in
Measure for Measure

I would not—though 'tis my familiar sin With maids to seem the lapwing, and to jest, Tongue far from heart—play with all virgins so: I hold you as a thing ensky'd and sainted; By your renouncement an immortal spirit; And to be talk'd with in sincerity, As with a saint.†
Scene 1.5 *

Look, here's the warrant, Claudio, for thy death: 'Tis now dead midnight, and by eight to-morrow Thou must be made immortal.†
Scene 4.2

Definitions:

(1) (immortal)
living or existing forever

or:

someone famous throughout history

or:

someone who will never die -- such as a mythological god
(2) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

More rarely, "The Immortals" denotes a military corps of the Persian Empire. The Immortals were so-named because each time a member of the 10,000 man corps was killed or seriously wounded, he was replaced by another man. They are best remembered in western culture for their role in defeating the badly out-numbered Spartans at the Battle of Thermopylae.