We've raised up "dime-sized" lionfishes, and they can indeed be touchy.
Tiny lionfishes can be very tuff to feed, and unless the crabs you're offering the fish are SUPER tiny (as in the size of its eye), it likely won't eat them. Your best bet would be to get the lionfish weaned off of living foods, but you should get it eating for you first.
If you have access to, or if you tank has a good pod population, esp.
Munnid isopods or
Gammarid amphipods, your fish will eat them with gusto.
Guppy or Mollie fry are good choices, as are small shrimp in the interim. You could even convert some to SW, or at least brackish water. If you feed live foods, be sure to enrich them with a good marine flake food at the very least.
Your absolute best bet for weaning the fish will be to DIY yourself a "stealth stick" (see the feeding article below), as you'll be needing to feed out pretty small food items for awhile, and the stick will work for the fish's lifetime.
Here's a good article on lionfish care, and another on feeding techniques. Give them a read and hit us back with any specific questions you may have:
Lions, and Turkeys, and Devils, Oh My! Lionfish in the Home Aquarium
Tools of the Trade: Equipment & Techniques to Convert your Fish onto Frozen
P. radiata is a really great fish. They're about as mellow as lions come, which means pretty darned mellow, and quite pretty. Being such a calm fish, they can be intimidated by fast movers or aggressive feeders, and IME, unless you target feed them, they likely won't get their fair share of the food.