The only lionfish that would be totally safe with the long nose hawk would be a fu manchu. All of the others could theoretically eventually eat the long nose hawk. If sized properly there may be a chance, but a risk. The longnose would have to be at least 3.5" to start. Any of the other lions will grow pretty fast the 1st year and would eat a small longnose. Lions can eat slender bodied fish more than half their size. What puffer? The blue spots tend to be nippers and it usually ends badly for the puffer.
Anglers will eat anything up to their own size, even the smaller warty would likely eat a long nose, A puffer would likely nip at a sedentary angler, and injuries usually end in bacterial infections and death. Anglers also require live food to have a chance at long term success which make a community tank with an angler challenging.
Dwarf and medium bodied lions also have feeding challenges that require some research for success.