Drive does not stay mounted
I tried to reproduce your environment using a VM (Mavericks 10.9.5).

I didn't get the same log errors as you did, but it didn't work neither: the (pre-)encrypted Logical Volume just doesn't mount properly.

I solved the problem in my VM by deleting the whole Logical Volume Group and rebuilding it but with an non-encrypted Logical Volume.

Then open the Time Machine preference pane, choose the Logical Volume as Time Machine backup volume and enable encrypted backups.



You will be asked to enter the passphrase twice and to enter a hint.



Alternatively you may try to mount the volume (after unlocking it) with 

diskutil mount 37D10BDF-AF34-4252-AAD7-41D18AFFF9AE