EWTN Catholic Q&A
last rites
Question from jimmy on 03-23-2017:

Can someone who is not Catholic request last rites?

Answer by David Gregson on 12-12-2017:

Not unless he were to request admission to the Catholic Church at the same time. If he were not already baptized, he could be baptized prior to confession, anointing of the sick, and Holy Communion. If he has already been baptized in another communion and doesn't have a baptismal certificate handy, he can ask to be baptized conditionally.

In short, a priest can administer last rites only to a member of the Catholic Church, but a person desiring last rites from a Catholic priest intimates a desire to be received into the Catholic Church. That can be done on his death bed, if time is short. And last rites would follow.