I also tried to figure out why this was happening.
It seems its a limitation of the engine and how the animation state machine was made.
The reason the first game didn't have this is probably just because it had way less animations
If you check the dlsite trailer you can see that the lag is present even there.
For reference, this is the state-machine of the player
Even at max zoom-out I can't display it fully. There is a lot more from all sides.
You can see that the basic states like Idle/Run/Attack are associated with a lot of states and those are the ones that lag the game. While the H-animation states are more one-way and thats why they don't lag (even if they did it'd probably not be noticeble tho so who knows)
It could also be that all the animations are on different files and loading/unloading them when changing states takes a hit on the fps.
Anyways, this is just a theory but seeing the state of this I don't think there is a simple fix for the problem and I its not likely that the devs can solve this either.