Usage: 3 forms in 4 verses
Form Translated As     In Verse(s)
επιθύσαι to sacrifice LXX.1Kgs.13.1
to sacrifice upon it LXX.1Kgs.12.33
επιθύοντασ sacrificing LXX.1Kgs.13.2
επέθυεν she sacrificed LXX.Hos.2.13

Liddell-Scott-Jones

ἐπιθύω (epithuō) to sacrifice upon G:V

ἐπιθύω,

(θύω A) sacrifice upon, [Refs]; sacrifice besides or after, τέλεον νεαροῖς ἐπιθύσας 4th-5th c.BC: Aeschylus Tragicus “Agamemnon” 1504; ἐπὶ δ᾽ ἔθυσα μητέρα 5th c.BC: Euripides Tragicus “Orestes” 562:—middle, Νέρωνι Τάλβαν . [Refs 1st c.AD+]

__II. burn incense, [LXX+1st c.BC+]: generally, offer on, ἐπὶ τοῦ βωμοῦ τὰς δεκάτας 1st c.BC: Dionysius Halicarnassensis 1.40 codices

LSJ Scripture Refs: LXX.1Kgs.12.33