snapshot may be a good fit in this case, but if you insist you can use
lvconvert to convert your linear volume to a mirrored volume. Once the
sync is complete, you can use the same lvconvert to convert the mirror
volume to a linear one.
But with this I loose the secondary copy.
It's not a good idea.
Backup and destroy backup :-)
If that is on a single PV, you can disconnect it to avoid it being
allocated by LVM for other things. I think, taking a snapshot and coping
it somewhere as someone said is a good idea.