In theory yes, but in practice: Not so much.

Even if we put aside GP's concerns, shooting big blobs of lava into space would require heating up the lava/rock in the first place. But this process doesn't happen on its own (through thermalization) given the average temperatures on Earth, meaning that the process of moving waste heat (from the environment, i.e. air/ocean) to the lava will once again decrease entropy (of the combined lava + air/ocean system) and you thus need to move the missing entropy elsewhere. (Meaning that you have to do work to accomplish this heat transfer / dethermalization and you will once again incur waste heat.)

Sure, we could also try to tap the heat bath of the Earth's core but then we would build a deep-Earth elevator to transport lava and solid rock (or, say, water) back and forth and GP's concerns apply once more.

There's another option, though: Don't build an air conditioning system/fridge – use thermalization with another (lower-temperature) system. That is, don't take lava (or anything that needs to be heated beyond ambient temperature) – "just" take rock at (Earth's) ambient temperature, move it to a lower-temperature $PLANET and then move cool rock from $PLANET back to Earth. I doubt this would be very efficient/fast, though.

In any case, the difference between the two approaches is that an air conditioner (or a fridge) cools things below ambient temperature and requires additional energy for that (which it will expel as waste heat), while the second approach "simply" moves energy from the heat bath that is Earth to some lower-temperature reservoire (i.e. $PLANET). If $PLANET and Earth were thermodynamically connected not just through the exchange of infrared radiation, this would happen by itself over time through thermalization.