The HomeLink menu coming up when exiting the garage is due to the GPS location appearing as if you’re coming close to your property. It could be due to GPS signal not having been fully acquired and the car thinking you are not at your location; then, when the signal is acquired as you back out of your garage, it thinks you just approached your location.
You may be able to simulate this if you could program your HomeLink far enough from your garage, where the car would show the menu when you approach and you are able to trigger HomeLink. This location would be such that in the garage, the car would think you are far from the programmed HomeLink location. This is a pain to do because it would require constant reprogramming until you got it just right. Also, if the distance is too great, you may not be able to go through all the programming steps. It also depends on when Lucid stores the GPS coordinates. If it does this as soon as you start the programming or when the programming completes and you verify that it works.