As far as I can see, the scope of lkl is pretty similar to the NetBSD Rump kernels (http://rumpkernel.org/). The difference there is that it has developed several back-ends already (directly on Xen, bare metal, GenodeOS, Hurd, ...).
So the crazy thing I just throw "out there" is : does it make any sense to build lkl on top of Rump (specifically, rumprun libc)?
At first sight it seems as convoluted as running Cygwin on top of Wine, but people do that sometimes...