If we consider that LSD mediates its psychoactive effects primarily through 5HT2A agonism, cariprazine would make things difficult to say the least. Additionally, the ultra-long half-life of cariprazine means two weeks wouldn't even be close to long enough to completely wash out. At the top end of the half-life of its metabolite didesmethylcariprazine (2-3 weeks) it could actually take as long as 4 months to completely wash out. However, relative to it's affinity for dopamine receptors, its antagonism of 5HT2A is moderate to low. I still haven't been able to find a good article that provides actual 5HT2A receptor occupancy (%) at each dose. When considering an optimal LSD experience, the lower the occupancy and affinity of the antipsychotic the better. This would rule out the -pine's and the -done's which almost always have a higher affinity for 5HT2A than D2/D3. However, aripiprazole, brexpiprazole, and cariprazine favor the dopamine receptors, with brexpiprazole having the strongest affinity at 5HT2A.
Another thing to consider is that the escitalopram is actually to his advantage. It increases serotonin levels and would theoretically amplify the effects of LSD. Caution should be used because a combination of an SSRI and LSD could cause serotonin syndrome. However, being on escitalopram may help to cancel out some of the 5HT2A antagonism of cariprazine. (However, there is quite a bit of evidence that escitalopram reduces HTR2A gene expression which theoretically would reduce the quantity and density of 5HT2A receptors in the brain. This could be problematic.)
I wouldn't encourage anyone to go off of meds without the supervision of a doctor even for a brief period of time. At the absolute least, he would require higher doses of LSD than most people to achieve the same effect. However, being off cariprazine for a few days may theoretically allow it to disassociate a bit from the 5HT2A receptors to allow for a better experience at more reasonable doses of LSD.