Maybe someone will come with smarter solution the thing I would do (although you have so many lanes) would be to
- Select the first event you want to snap to and press L so that your cursor will snap at the beginning
- Select one by one the events on the lanes and press CTRL + L to move to the locator.
Alternately you could also copy the start time of one event and paste it to the others but I find the first solution perhaps easier.
One cool feature request would be to maybe when pasting the Start time to be able to specify if you want it relative or absolute (a similar behavior is done with MIDI velocity where you CTRL+Click the velocity box and all the events are set at the same velocity)