Same material, according to Adler, in the Ambrosian Lexicon (484, 414).
[1] The primary headword, evidently quoted from somewhere, is masculine accusative singular or neuter nominative/accusative singular of this adjective. The glossing interprets it as if derived from δαίω , "burn"; however, the only entry in LSJ for ἀδαῖος (web adress 1 below) connects it with ἄδην , "sufficiently", and translates it as "producing surfeit", citing Sophron 137.
[2] The individual in question is probably the C4 BCE Macedonian general of this name, nicknamed Rooster. See principally Theopompus FGrH 115 F249 (quoted by Athenaeus), with N.G.L. Hammond & G.T. Griffith, A History of Macedonia 2 (Oxford 1979) 441. But for another possibility see under alpha 594.