Hi
In order to run SE it will need to create a snapshot, this can be big sometimes especially if you are doing dedup and compression.
I seem to remember dedup is not recommended for Domino vols, but you can't have compression without dedup although you have dedup without compression.
Have you got thin prov'd on both the volume and the lun? that can save you up to 50% of the space before any SE.
Also in Domino there are something you can do to single instance attachments etc, I think it's called DAOS.
If all else fails, you may need to at least temporarily grow the volume or may be delete some snapshots.
If you are seeing lots of free space in the host but not on volume / lun, a defrag in Windows or "space reclaim" within snapdrive can help, the later does require low or no date change rate.
Hope this helps.