If the cylinder doesn't turn when you pull the trigger, the gun probably needs a new hand. That may be what H&R call a lifter. If the trigger doesn't return, it probably needs a new return spring.
Check out this parts shop:
Numrich Gun Parts Corp. - The World's Largest Supplier of Firearms Parts and Accessories
That link takes you to the H&R page. I don't know how a Premier differs from a small frame break-top .32, but maybe the illustrations and parts photos there will give you some ideas.
That's about the limit of my research ability for non S&W guns. Good luck with your project. If the gun is generally in good shape, I think it may not need much to put it right.