I have IR tint as well and that will help slow down the rate at which heat builds in the cabin but will not eliminate the heat build up. The air in the cabin will continue increasing so long as the car is exposed to direct sunlight.
Now, having said that... I was at the mall for about 3 - 4 hours (yes, take pity on me) during the middle of the day when the temp was 111. Prior to returning to my car, I used the app to check the internal cabin temp, which was 134. I turned on climate control from the app and headed to my car 15 - 20 minutes later and arrived to an 88 degree temp, which felt perfectly fine to me upon entry. I kept the A/C on and within another 5 minutes after starting my drive I was down to 78. I normally keep my house at 81, so I felt the overall experience went quite well.
You could crack open your window(s), which will help believe it or not even when it's 115 out. As I said, that will allow air above that temp to escape the cabin. For me, I would need to be in a location that I felt comfortable leaving a window open.
I can't speak to comparisons to Tesla, other than to say that I suspect there is much more cubic space of air in the Lucid and as such, it will take more time for your A/C to cycle that out assuming the same A/C performance between the two vehicles (which may not be an accurate assumption).
Personally, and I've articulated this on another thread, I think the the A/C is under capacity on the Lucid and should be addressed. I cannot imagine what the Saudi's are doing in that heat.