A better live food to tempt the puffer, IMO, would be ghost shrimp. I agree that it is not good, and certainly not necessary, to feed either fish live feeders. The majority of feeders available (guppies, goldfish) are NOT a normal diet and do lead to health problems, in addition to overfeeding (and an unecessary expense). Lionfish, once the get eating, are usually not fussy at all and you can insure a varied diet....once given live food, they can become finicky.
There are a number of posts on this, so a search may be worthwhile. Also try posting in the agressive forum.