I have Pityriasis lichenoides / PLC a rare skin disease and I really want to freeze my fat.

Is it possible to do CoolSculpting (Fat Freezing) if you have a chronic skin condition like Psoriasis, Pityriasis Lichenoides Chronica or Lichen Planus?

If you have active skin lesions in the area that you want to be treated, I would be hesitant to treat as the CoolSculpting could cause a flare of your condition. This would be most important for conditions that "koebnerize" (show up in areas of skin trauma). Both Lichen Planus and Psoriasis are known to do this.
PLC is less likely to have this phenomenon occur.

I recommend working closely with the doctor that you choose to go to. Discuss the possibility of a flare of your condition (and no, I don't think there are more risks than a flare). And decide if, for you, doing CS is worth the risk.