This is a great idea!
SYD was obvious, and it appears that OW is more likely than *A despite the old BD Silver status. The 6:30am flights are boarding, so it's around 6:00-6:15 and the next OW flights are leaving in the 7:15 area — only an hour, so not enough time to enjoy the lounge properly and have breakfast. There are only two other OW flights, Japan to Narita at 8:15, which is doable, or Qantas to Christchurch at 9:15 The latter does not seem likely, unless he's flying on from there to somewhere more exotic and is just teasing us, so by a process of elimination — ta-da! — he must be on JL 772!
Well I won't say whether you are right or not ... yet. You should be able to tell from the Part 2 photos!