Cf. the same phrase in Hesychius s.vv. διψάς, δοχεών, δόλου τραπεζα, Διόσκουροι, δεσμόν, and especially δοχή, σημεῖον ἐν θυτικῇ ἔχις. ὕδρα. καὶ σημεῖον ἐν θυτικῇ ἐπὶ τοῦ ἥπατος ("mark in sacrificial practice on the liver").
First thing you want to check when you've opened up your sacrificial beast: the liver. Watch out for those portentous marks.
Hesychius has eleven entries involving the word θυτικῇ in sections alpha through kappa, usually in the formula σημεῖον ἐν θυτικῇ. This could be a fertile field for a dissertation on ancient sacrificial practices, significant not only for classicists, but for anthropologists as well — supplementing the anthropological work of Hubert & Mauss.