Parashas Acharei Mos · Passuk 16:09
Chabad.org — English translation + Rashi
Torah Temima points to Yoma 40b.
English: “Upon which the lot came up” — once it has come up, it need no longer remain upon it [until slaughter].
Lot need not stay on the goat
The assignment is fixed when the lot is drawn; the token need not stay on the animal until slaughter.