Mine have always grown fat & sassy on mysis & blood worms & brine. Other local reefers have told me that if their LM blennies don't switch to supplementing with frzn foods, then they always starve to death.
Maybe try growing some grape or feather caulerpa, since most herbivores love that stuff. If I toss in a fist sized clump in the evening, by morning not a stem is left after my tangs & angels are through.
JME
Anthony
In most of our tanks, we would have a hard time growing enough food for a hungry LM blenny, since mine will eat almost constantly.