Heat your Airship - or reduce your dead weight loads
Have a material that can withstand extraordinary heat, and a way to vent heated air - safely
If you heat the gas inside your airship, the gas would decrease in density. You need to stop the airship from expanding (and thus exploding), so you need to control also the amount of gas in your airship too. If your hydrogen/helium was heated inside the airship (without exploding), and vented out as required, your airship would have more lift. The mechanisms required to do this need to weigh less than the benefit of heating the gas though.
Increase boyancy by decreasing your 'dead' weight
LZ126 used 23000kg of gasoline on a typical cross-atlantic voyage. Imagine if all this weight was saved by having a new fuel source that was much lighter! Maybe in your world gasoline has a quarter of our worlds weight.
Also, having gondolas that were made of a lighter material will help too, having structure much stronger and lighter than aluminium trusses, or the skin itself could also be much lighter.
You could also consider other factors to make Airships more desirable. These include:
Make the world completely windless
Wind is a major impediment to Airships, being unpredictable, influencing your course, and also capable of destroying them easily. If wind did not exist in our world airships would be much more controllable and safer, both cruising and docking.
Make a flexible material that can expand and contract the volume of the airship
Your lifting gas is actually dependant on volume. If the skin of your airship is variable easily, you could control the pressure inside and thus the boyancy. Having such a fine level of control would enable Airships to change the altitude without the use of 'forcing' it down using engines. Controlling volume would also reduce the need for ballast - a major 'dead weight' that works against your boyancy.
Docking would be much easier too - which of course was a dangerous exercise and another major source of airship deaths.
Make airplanes difficult to fly
A major impediment to Airship development was simply that airplanes became cheaper, safer, faster and more reliable. By removing fixed wing aircraft from history we would likely still be using Airships today. Perhaps a fuel is lacking in your world meaning airplane engines did not have enough thrust to create lift, or there were no materials rigid enough / light enough to have a rigid wing, or simply they hadn't been invented yet.