Alright so update now that I had some time.
It seems like it is happening when FGU has to load a lot of things. When I was experiencing it in a story section when writing, it had 12,822 characters. Those made up 2,347 words over 160 lines. It would have the occasional lag when typing in that. When I made a new story module, the lag was minimal. So I would think the lag happens as you get more and more characters written in a story module.
Another example of the lag happens on character sheets. If I am opening up a Player Characters Action tab, it will take a few seconds to load. This is faster after it loads for the first time. It can be a bit annoying though waiting a few seconds to load a prepared spellcaster who is a high level and thus has a lot of spells to choose form. The less options in the Actions tab, the faster it loads. There was no lag in Fantasy Grounds Classic when loading it. Really this applies to every tab, but the Actions tab is the longest. It does take a second to load the Skills tab as well.
Basically, FGU doesn't feel as "snappy" as FGC does right now since this doesn't happen in FGC. The issue with lag when typing in a story section or on the character sheets.
This is all for 5e.
FGU v4.0.3
5e Ruleset v3.3.12
No Extensions
No Themes.