I have to disagree with placing triggers with any lionfish. Triggers are notorious for nipping the spines off of the lions then harassing them to death. Puffers are a bad idea too. Not only because they nip too, but they are rather slow to move out of the way and might be accidently stung by the lionfish. Not to mention that neither one would do well in a small tank.
In a 37g, I wouldn't recommend any tang (although they are a good match for lions), but a larger clown like the tomato would be good, or a flame hawkfish would go good too. Just remember that lionfish have extremely large mouths and any fish or shrimp that can fit in there, they will try and take! Slender bodied fish like the blennies, gobies, etc...IMO it's only a matter of time. Try and go for fish that are more laterally compressed rather than long and slender. Also remember that lionfish will put out quite a bit of waste, so don't overstock the tank.
You can do a search on training lionfish to take "dead" foods. It is a very good idea to switch him over while he is the only fish in the tank (it makes it easier to do!). It is very important that you don't feed your lionfish for the long term on freshwater fish! Very bad for them, even guppies have high fat contents and lack the HUFA's that all marine fish need.
Good luck to you and your new fish!
.....just my 2 cents.......