Howdy Rob! Living DNA tests a pretty good selection of SNP's, enough to be able to determine a fairly detailed mtDNA haplogroup for most westerners. For me, they came up with K1c2, which I found rather impressive, since that represented a whole lot more dollars spent at FTDNA, to come up with the same.
The fact that they did not give you anything beyond K1 would imply you are in a less 'popular' branch, one which they did not have SNP's for. You're going to need YFull's attention to get your true haplogroup. A caution though - currently, YFull is going through a huge redo of the mtDNA tree, and making changes constantly. Haplogroups near mine have already been renamed 3 times, and they are clearly not done! It may be another month or two before it stabilizes, and you can begin to trust the haplogroup they assign you. (Actually, that's something I should warn everyone about, that has uploaded to YFull!)