ἀπολαγχάνω
From LSJ
ἐπ' αὐτὸν ἥκεις τὸν βατῆρα τῆς θύρας → you've come to the crux of the matter, come to the point, hit the nail on the head, you've come to the very threshold of the door, you are come to the very threshold of the door, you've arrived at the truth of the matter
English (LSJ)
A obtain a portion of a thing by lot, λαγχάνειν ἄπο μοῖραν ἐσθλῶν B.4.20; τῶν κτημάτων τὸ μέρος ἀ. Hdt.4.114, cf. 115; τὴν Ταναγρικὴν μοῖραν Id.5.57; τῆς γῆς Id.4.145; μόριον ὅσον αὐτοῖσι ἐπέβαλλε Id.7.23; ὡς ἀλλὰ ταῦτά γ' ἀπολάχωσ' οἴκων πατρός that they may obtain .., E.HF331; cf. Antipho Fr.63, Leg.Gort.5.4, al. II fail in drawing lots, ἀ. κριτής Lys.4.3, cf. Plu. Cat.Mi.6, 2.102e: generally, lose one's all, be left destitute, E.Ion609.