Typically there are different requirements.
I think the rules says that if you are a OneWorld Sapphire or Emerald member, you may use any business / first (for Emerald) DEPARTURE lounges on the day you are traveling on a OneWorld flight.
Similar thing with Star Alliance.
For example, the BA arrivals lounge in LHR is only for business and first class passenger or BA Gold or QF top tier members. NOT all OneWorld Sapphire or Emerald members.
It is even worse with UA's arrival lounge. Only business (no upgrades) or first class passengers can use the arrival lounge. Not even United 1K members can use it.