It's vary lag but I like this game.
Not that I can help solve the lag but what hardware/OS are you running this on?
I've been running this on an admittedly out-of-date system in this day and age and I haven't had any lag.
I can't recall all the hardward off the top of my head but a Gforce 1080TI with 2V-RAM, 40 DDR4 2350hz(??) RAM, I think an I7 8core CPU on WIN10 home edition. (likely overkill for this game tbh)
Happened to me, the first time I started the patch, but only when my laptop wasn't plugged into the power supply (probably some power saving that limited processing power). I noticed however that looking in the direction of the new fire pillar structure, reduces performance significantly, if you have limited pp.
If the game runs fine in other locations, such as the home island, these new structures might be the problem.