During WW1 Zeppelins began their missions with Hydrogen cells at 33% full. How did this provide enough lift to get off the ground?
The gas bags always contained close to 100% hydrogen. No air was supposed to be in them. On the ground, the bags were only partially filled because of the high air density and pressure. The rest of the internal volume of the Zeppelin was filled with air which could enter and escape the hull through the many gaps and venting openings.
Compare that to a weather ballon. On the ground, the big envelope is nearly empty and only a small bubble of lifting gas (today mostly helium, but hydrogen would work even better) sits at the top. Only that the nearly empty ballon is in clear sight, while in a rigid airship the half full gas bag is hidden behind the rigid hull covering.
One cubic meter of hydrogen weighs only 90 grams compared to one cubic meter of air at 1.225 kg under standard atmospheric conditions. With the same amount of hydrogen a balloon will have the same lift, regardless of altitude, because its lifting gas will displace a bigger volume but the same mass of air as it expands with altitude. With Zeppelins, fine tuning of lift by adding dynamic lift is possible but limited to maybe 5%-20% of the ship's mass (more for smaller and faster ships and at lower altitude). By growing larger, the mass to volume ratio of Zeppelins decreased, so the latest WW I ships could be built light enough to fly with their gas bags only one third full.
Civilian airships rarely flew higher than 2000 m high and had to circumvent higher mountain ranges because they filled their gas bags to maybe 80% on the ground. Flying higher was not considered worth the reduction in payload and fuel that would result from less lifting gas.
Compare that to the wartime Zeppelins. They were in a continuous arms race for higher altitude with the British aeroplanes which were sent out to chase them. And until 1918 the most modern Zeppelin designs  were ahead. The limited altitude of older ships also meant that many were scrapped after one or two years of service. The table below shows the maximum altitude at which the gas bags were filling out the available volume of the ships. The list below gives the maximum altitude of the best ship of each series and the density ratio shows the degree to which the gas bags could be filled on the ground to achieve that altitude. Note that they still carried tons of water ballast and ordnance when flying that high.

LZ 112 tried with speed what could not any longer be achieved with altitude: It had 7 more powerful engines where older ships had only 5 and could cruise at 131 km/h as opposed to the 100 km/h of the older ships. The diminishing returns of flying higher and the stress of spending close to a day at -40°C and without a pressure cabin or a pressure suit made higher flight altitude impossible. What also held progress back was the size of airship hangars: Since LZ 62 the maximum diameter could not grow beyond the 23.9 m of the last wartime ships, so their volumetric efficiency went down when they grew larger by adding length.