Right-clicking on a User Collection and selecting Delete… will cause the Delete confirmation prompt to pop up:
Click the Delete button to delete the User Collection in Lightroom.
Deleting a User Collection in Lightroom (as is Deleting a User Collection in Photosmith) will not cause the photos contained in a User Collection to be deleted. Also, deletes are never propagated during sync.
A User Collection deleted in Lightroom will not cause the corresponding User Collection in Photosmith to also be deleted - this must be manually done also in Photosmith, as described in Section 188.8.131.52.