The current lkl build logic breaks incremental builds, in that a source change in base kernel won't regenerate tools/lkl/ binaries. This appears to be due to the Makefile dependency chain, where the $(OUTPUT)lib/lkl.o: target is responsible for calling make and make install for the parent base kernel directory.
I've played around with a few hacks to workaround this, but I think the cleanest option might be to conditionally traverse into tools/lkl as part of the regular ARCH=lkl parent kernel build process.