Why is it "paw chaH" and not "lupaw"?
The prefix lu- indicates that the subject is "they" and the object is "him, her, it".
But they don't "arrive it"; they simply arrive. There is no object here.
So you need the prefix for "subject = they; no object". The prefix for that is nothing at all -- "they arrive" = paw.
The subject pronoun chaH is not needed, but can be included for clarity, to disinguish "they arrive" from "he/she/it arrives", which would also be paw.