Here's the verse again:
ὅτι κατηριθμημένος ἦν ἐν ἡμῖν καὶ ἔλαχεν τὸν κλῆρον τῆς διακονίας ταύτης
for numbered he was among us, and he obtained a share of this ministry
The form ἔλαχεν is 3-S, aorist active indicative of the verb λαγχάνω, 'I cast lots', 'I obtain by lot', 'I have a share', and so on. This verb is known from Homer down, but is seen only four times in the New Testament, so we don't get an extensive look at the possible meanings there.