There seems to be a problem with the most recent update of SE (0.6.91) where trains no longer enter the elevator or just crash the game when doing so.

MainLoop.cpp:1284: Exception at tick 2566374: The mod Space Exploration (0.6.92) caused a non-recoverable error.
Please report this error to the mod author.

Error while running event space-exploration::on_tick (ID 0)
The mod LTN Manager (0.4.15) caused a non-recoverable error.
Please report this error to the mod author.

Error while running event LtnManager::on_train_created (ID 68)
LtnManager/scripts/ltn-data.lua:1236: attempt to index local 'trains' (a nil value)
stack traceback:
LtnManager/scripts/ltn-data.lua:1236: in function 'migrate_train'
LtnManager/scripts/ltn-data.lua:1256: in function <LtnManager/scripts/ltn-data.lua:1249>
stack traceback:
[C]: in function 'create_entity'
space-exploration/scripts/space-elevator.lua:684: in function 'space_elevator_teleport_next'
space-exploration/scripts/space-elevator.lua:1353: in function 'space_elevator_tick'
space-exploration/scripts/space-elevator.lua:1380: in function 'callback'
space-exploration/scripts/event.lua:15: in function <space-exploration/scripts/event.lua:13>

This could also be related to the update frequency (ticks). I changed this value from 2 to 50 and now trains no longer have a valid route through the elevator. Changing its back to the default value restores the behavior back to normal.

The stacktrace neither contains code locations from LTN nor from this integration mod. The crash happens in LTN Manager. It's odd though, I'm running a game on SE 0.6.94 with LTN Manager and that works just fine.

I'll have to investigate your second problem related to lowered update frequency.

To the first issue I can just say it happened when I toggled the LTN Button in the Elevator and opened the UI again later. Altough the error did not occour again since then and I think it was patched by either SE or LTN indireclty in the past days.

I tried to reproduce problems with the update frequency on my small test map but if I set it too the maximum of 60 ticks the only thing that happens is that the train schedule is modified to include the elevator stops roughly 1 sec after the train leaves the depot - which unsurprisingly is roughly 60 ticks.