EDIT
What I meant by outting it was to place the control switch: 001 ON command outside the conditional branch in the event. This, as Nouman pointed out, would make it so that jumping would be available everywhere once you've stepped on the event, which you don't want, thus it would not work. Thus, just ignore that first post of mine.
END EDIT
This being the case, I'd prefer not to use a common event then, because as it is you can walk on to the event, then walk off of it and jumping wouldn't deactivate. I'd just use local events (Action Key activated) like this: (this only works if you set the lilypad to passable. If you have some reason for them not being passable, post and I'll rework it)
On the left bank
Conditional Branch: Player is facing Right
Set Move Route: Player
Jump (+2, +0)
Branch End
On the right bank
Conditional Branch: Player is facing Left
Set Move Route: Player
Jump (-2, +0)
Branch End
on the lilypads:
Conditional Branch: Player is facing Right
Set Move Route: Player
Jump (+2, +0)
Branch End
Conditional Branch: Player is facing Left
Set Move Route: Player
Jump (-2, +0)
Branch End
It probably looks confusing so I included a demo. It looks like it would be a lot of work because you would have to put events like this everywhere you want to be able to jump, but it's just copying and pasting. Plus it removes the necessity to conditionalize if the player decides not to jump after he approaches the place where he can. Again, the lilypad has to be set to passable in the database before this will work.