The lag is due to the core system being mess up not due to how many players are playing in a giving day. In ffxi i play in bahamut where it was 3-4k in prime hours i play without issue. FFXIV have more problem then just gameplay the servers--Core system--> all mess up they need to upgrade there servers and fix the core system to fix the lag issue. Without a core system update and server update they can't even make it so we could trade more then 8 slot per trade or allow us to change price of our item without taking it out and reselling it.

Top of all that lag issue could also be your computer and many other stuff so at this point it can be anything or everything.