The headword adverb is well attested from Josephus (Jewish Antiquities 19.301) onwards. The second word cited is etymologically unrelated to it, being derived from the root -mel- ('care') rather than -mell- ('be about to act, postpone'). There seems to be some confusion over that distinction here and in other lexica (see note 1 for an example of another lexicon spelling the headword with one -l-).
[1] = Photius alpha1184, and Synagoge alpha378 (Codex B: alpha1040), s.v. a)me/hti [sic]; cf. Hesychius alpha3574. See also alpha 1560.
[2] More fully in the De syntacticis alpha71 Petrova (= Lexica Segueriana 129.26-30): genitive of thing but dative of person; Arrian (Anabasis 1.24.1) is quoted for the dative, and Appian (fr. 21 -- not in fact including the present headword, but the related verb h)me/loun) -- for the genitive.