If W in the OP means the premium economy cabin, note that there are some airlines that do grant lounge access for passengers ticketed and confirmed in this cabin class or that permit such departing passengers to pay extra to access the lounge.

UA has lounges at EWR and gives access for departing passengers confirmed in international business class. However, you need to check whether MBJ is considered to be international for the purpose of lounge access, which might depend on whether the flight is marketed as business first etc. Some airlines make exceptions for Caribbean flights and do not give lounge access for these leisure routes.