Is there any way to grill the lettuce in advance?

Agree with Nancy. The grilled lettuce will not hold well if they sit for hours.

Since the lettuce only grills for at most 2 minutes, it might be a better plan to prep them to be grill-ready and the dressing in advance. Then grill them right before you eat.

Lettuce hot off the grill can be great; grilled lettuce sitting several hours less great.
If you mostly want to take a grilled salad to the pot luck, use a recipe featuring other vegetables, like corn and sweet peppers.
If you mostly want to take a Caesar salad, use a classic (ungrilled) recipe.