Could some combination of a partial vacuum and hot air substitute for helium? Of course you'd need some ultra light superstructure to maintain the giant vacuum, but that's "just" engineering.
Air at 175C has about 40% the lifting power as the same volume of helium (or hydrogen). That is very hot, and requires a lot of energy to sustain. Lower temperatures will reduce the lifting power.
That's why thermal airships (https://en.wikipedia.org/wiki/Thermal_airship) are very uncommon, the lift inefficiency means the structural weight doesn't scale, and the cross-section makes them very hard drive and control.
I guess because airships were already out of fashion by the time the atomic age came, but a thermal airship where the heater is just a radioactive pile seems like a super simple design.
The enormous bulk of the airship is an advantage in this case, you can reduce the amount of shielding you need by keeping the radioactive stuff way off on one side of the vehicle and the people on the other. Of course it would still be a nasty cleanup effort if your airship crashes, and you have to deal with radioactive materials when landed or when doing maintenance. From a practical standpoint there are issues, but in theory the concept works.
A reactor powered thermal airship is a fascinating idea! I'm skeptical that it could work though. Some quick web searching suggests that 3 MW burners for hot air balloons is fairly typical. I'm not sure how light and powerful a reactor could be made, but wikipedia says the Convair NB-36H had a 1 MW air-cooled reactor weighing 16,000kg. That reactor definitely wouldn't work then, too heavy by far and not enough power output. But that was a prototype reactor in the 50s.
Also, shielding seems like a big concern even if the reactor can be built light. To stop neutron radiation you need light nuclei like hydrogen, making water or concrete (containing water) popular choices. These are heavy and bulky though, not conducive to airships.
That's why my consideration for shielding was mostly just distance. Certainly a concept for a time when people were more cavalier about radiation safety.
That’s where the vacuum comes in. Extract half of that hot air, seal the container, and you have 70% of the helium lifting force. (Math may be wrong there but you get the idea)
Really you don’t need hot air at all. If you have a massive vacuum contained by a rigid shell of some super light super strong material you’d be set. Density of air at sea level is around 1 kg/m^3, so 100 m^2 of material lifts 3 tons. Assuming one ton for material, one for propulsion, one for cargo, you end up needing a shell material that can weigh up to 1 kg/m^2 and can hold a near vacuum. Like I said earlier, “just” and engineering problem.
The good news is economies of scale are on your side: 10000 m^2 of shell can lift 3 thousand tons. At that scale your shell can be up to 300 kg/m^2. A bit more reasonable.
