I think the issue is that the weight of the lid and top grill pressing down on the steak squeezes a lot more juice out than if you grilled the steak on regular grill that heats from below.
You usually press down on it or use a weight with a regular grill. You want a crust from a Maillard reaction on the outer surfaces, with a less-cooked interior.
I do not do that. I use the reverse sear technique popularized by Kenji Lopez-Alt. This involves heating the steak to near-doneness over indirect heat, followed by an intense sear over direct heat. A brief rest period in between allows an even better sear, as the surface has a bit of time to dry out and the internal temperature to drop a bit, enabling more time over high heat.