Would like to second this question.
I'm also flying from HND (internationally) in PE, with JMB Sapphire status (and JGC, but not JGC Premier just yet).
I gather from earlier reports that the CX lounge might be my best option? JAL seems to be recommending the Sky Lounge Annex for the time of day when my flight departs... which doesn't seem to be a nice lounge at all.