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As many of us probably know airships were one of the great forms of transportation in the 20th century but a great hindrance to their development was weight. In a world I am currently constructing the gravity is 1/3 as that on earth so metals and material are lighter but have the same strength as on our world. They are so light that steel weighs the same as aluminum here on earth and can be used in airship construction. Because of the reduced gravity airships can now carry bigger loads per same volume of gas here on earth but there is one detail that eludes me. Would lifting gas have 3 times the lift per 1,000 cubic feet in this lower gravity environment or would it stay the same as here on earth? Note that although the gravity is 1/3 the atmosphere is the same pressure, density and composition as here on earth. Also would metal retain the same strength in a lighter gravity world as I do not know the effects of lighter gravity on metal production.

Actually, they lift exactly the same amount of mass, even though it may weigh less because of the decreased gravity.

Lifting gasses generate lift via buoyancy. Basically, they displace heavier fluids with lighter ones. The most energy efficient way to do this is for the heavier fluids to flow underneath the lighter ones. However, since the lifting capabilities are based on the weight of the displaced fluid, which is also 1/3 lighter, your lifting gasses all produces 1/3 as much lift. The weight of the airship is also 1/3 as heavy, so the effects cancel.

If you want lifting gasses to be more effective, what you want is a more dense atmosphere at the same pressure, such as having lots of sulfur hexaflouride in the atmosphere (which is decidedly unnatural, so you'd have to work at it). Alternatively, if you had a hard-shell around the lifting gas, rather than the more typical fabric, you could evacuate the insides. Then all you would need is an atmosphere which is more dense, regardless of what pressure it's at. A thicker atmosphere would be sufficient.

Ironically, that calls for a planet with more gravity, to hold onto the atmosphere better.

Believe it or not, airships would be harder to make on a lower gravity world, not easier.

Hot air balloons and airships are able to float because their systems have a lower density than the surrounding air. This is why they can only fly to a certain altitude: eventually, they will reach a point where the atmosphere is too thin to allow them to rise.

In a world with only 1/3 the gravity of earth, the atmosphere is going to be significantly thinner at sea level than on earth itself. That means that any airship will need to either displace a larger amount of gas (with a bigger balloon) , have a lower mass, or use an internal gas with a much lower density than the surrounding air.