Weird solution, but it works: https://www.reddit.com/r/PSO2/comments/gsn90o/workaround_fix_unbearable_lobby_lag/
Looks like the official launcher is adding some command line parameters "+0xHEXSTUFF -optimize" and when launching it without the launcher or renamed, it uses "-win10" instead, which eliminates the lag.
dnb321 on Reddit found out the parameter thing: https://www.reddit.com/r/PSO2/comments/gsn90o/workaround_fix_unbearable_lobby_lag/fs8k1qp/
Krisan-Thyme figured out the launcher was doing some oddities.
Hopefully, the development team will remove the offending parameters from the launcher.
To me, just looking at the parameters, looks like they left some debug switches or something on, which is causing the lag in the first place.