When you try to delete a partition which was part of a broken mirror set, you receive:

The drive cannot be locked for exclusive use. Please check to see if some applications are currently accessing the drive. If so, close them and try again.

None of the standard reasons for not being able to lock a volume exist:

A paging file is on the volume.
 A program that was started from the volume is still running.
 A program that is running has loaded a .dll file from the volume.
 A program has a file open on the volume.
 A program's current folder is on the volume.
 A Service has a lock on the volume.
To resolve this issue, use Disk Administrator to select the partition you wish to delete. Use Tools / Assign Drive Letter to click Do not assign a drive letter. Press OK. You should now be able to delete the partition.