"Lagging" as in "uses an inordinate amount of script time all the time"? How many trains and LTN stops in total?
What this mod does is collect LTN delivery data when LTN publishes them via events and then sets up the extra schedule entries to drive through the elevator. That activity should hardly be noticeable.
Actually driving through an elevator will indeed cause a short spike in LTN because that triggers a delivery update for every carriage that passes through the elevator. There's no way around that, LTN needs to know that a delivery has been switched to a new train on a new surface and update its internal structures.
I have no idea how any of this affects an at first glance totally unrelated mod. Could it be that what you are seeing with the tweak mod is its ore-update after a configuration change (I took a quick look through its control.lua)? Does that settle back down after a while?