Generally, where there is an arrivals lounge it's at the airline's hub, and quite often isolated from the benefits of the associated Alliance. To make it worse the lounge will most likely be landside.

When you are airside, lounge entry is generally governed with reference to your departing flight. No-one guarding access to to the lounge is interested in how you got there....

I've hedged all that with "generlies" etc because there are exceptions - though non will apply in the OP's situation