It's one Chase lounge visit per year, but inasmuch as there are only two Chase lounges open we do not yet have reports to verify if their software can recognize if you have already used your visit at another location.
My wild guess is that PP holders will be denied entry at the second lounge. A big part of the marketing here is to tempt those PP holders to get a Chase Sapphire card. If it’s done right, the second attempt should trigger a friendly “sorry, but we would love to welcome you next time with a Chase Sapphire card. Would you like an application? We have a nice bonus offer right now.”