An entry not literally excerpted from the Lexicon Ambrosianum: Ambrosianus B12 sup. fol. 76v has h)ggu/a: e)peti/qei, e)bebai/ou, 'was giving as a pledge', [meaning] was offering, was guaranteeing. Photius, Lexicon eta19 Theodoridis and Herennius Philo, De diversis verborum significationibus eta88 Palmieri (where perhaps the Photian entry is taken from) have the gloss w(molo/gei dw/sein, 'was agreeing to give'.
h)ggu/a is imperfect indicative active, third person singular, of e)ggua/w (epsilon 169), a verb commonly used in the classical period. In this precise form it occurs twice in Isaeus (3.45 & 70) and twice in Demosthenes (41.6 & 16).