luckily
From LSJ
Τραφὲν ὄρεσι καὶ φάραγξιν ἀγρίαις, κήρυξ πέφυκα τῆς λόγου ὑμνῳδίας. Φωνήν μὲν οὐκ ἔναρθρον, εὔηχον δ' ἔχω (Byzantine riddle) → Raised in the mountains and wild ravines, I have become the herald of hymns that are sung. I have no articulate voice...
English > Greek (Woodhouse)
adverb
P. and V. εὐτυχῶς, εὐδαιμόνως, μακαρίως.
as luck would have it: P. κατὰ τύχην (Thuc. 3, 49).