"Lycidas" l. 70 (1638). A 1619 play thought to be written by John Fletcher, Sir John van Olden Barnavelt act 1, sc. 1, refers to "the desire of glory (That last infirmity of noble minds)." That play was lost and not rediscovered until 1883, so Milton's parallel words were coincidental.
Quoted in Thomas Moore, Letters and Journals of Lord Byron (1830). Byron wrote this in his Memoranda after the first two cantos of his poem Childe Harold's Pilgrimage were published in 1812 and became sensationally popular.