Quick one re lounge access.

Flying into Seattle next summer using a 241 in J. We are booking flights to Hawaii on Alaska. My preference would have been domestic first for that leg just because it’s a very long trip for us and I wanted to guarantee access to the Alaska Lounge but no miles availability in F. If I were to book using miles economy from Seattle to Hawaii would BA allow me access to their lounge given I’ve come in on J regardless of the domestic economy flight to Hawaii on a separate booking? I think the answer is yes but want to check. I’d have preferred a lounge with showers but unsure I’ll get into any other oneworld lounge… happy to be corrected