In the majority of cases yes, but that hasn't been my experience absolutely everywhere. It is also the case at some airports that a OWE with a (P) ticket may actually have access to better lounges via their status than the lounge QR are sending its J passengers to.

Anyway, to avoid getting into a list of wheres and what ifs and exceptions, the main point is that applicable OW status pax will get some form of lounge access irrespective of travelling on a (P) ticket.

And yes, it's always sensible to ask about the arrangements at check-in (if the agent doesn't tell you first), even if travelling on a lounge inclusive ticket.