Helium and hydrogen have no power to lift anything.
A lighter-than-air craft is able to fly because it is lighter than air (i.e., it weighs less than the volume of air that it displaces.) Helium or hydrogen are used because they fill the space, and they are lighter than air.
If you compress the lifting gas, that means you are putting more of it into the envelope. More weight. That's the opposite of what you want. You want the least weight possible. The ideal would be to "fill" the envelope with vacuum. Having no gas in the envelope would mean having no weight at all.
Unfortunately, any "container" for vacuum must be strong enough to withstand the external atmospheric pressure without being crushed. The lightest possible "container" for a given volume of vacuum ends up weighing far more than a balloon with the same volume, filled with helium---far more than the weight of the air that it displaces.