little bit of common sense required here
liquid LPG injection systems are available these days- as the LPG is port injected, it changes from a liquid to a vapour, and the change of state of the liquid to a low pressure gas results in a drop in temperature. this also sucks heat out of the combined intake charge in the inlet manifold (latent heat of evaporation). it turns into gas instantly
same would happen with liquid nitrogen. but it wouldn't benefit power, because nitrogen isn't combustible and would merely take up space that could be occupied by oxygen
the reason NOS gives a power increase is because its N20, and during combustion the oxygen molecules are stripped off the compound to massively aid the combustion of the incoming fuel/air charge