What kind of sauce would you use for lobster ravioli? I don't want to overpower it with a tomato-based sauce.

I like them in a brown butter/sage sauce. But I've also had them in vodka cream sauce that were pretty wonderful.

What about brown butter sauce?

http://www.epicurious.com/recipes/food/views/Sweet-Potato-Ravioli-with-Brown-Butter-107701

A cream sauce. Or a butter/wine/lemon sauce.
A drop or two of vanilla pairs well with lobster; just a hint for a back note of vanilla.

(When I steam my lobsters, I put a tsp in the steaming water)

White wine, butter and a hint of fresh tarragon.

You could serve it soup-like in a light broth instead of a sauce, maybe a chicken / saffron sort of thing, or an herbed broth.

I'd try a play on dymnyno's vinaigrette from this recipe. It's heavenly. I'd just reduce the amount of acid, and probably use butter in place of the olive oil. http://www.food52.com/recipes/9416_citrus_salad_with_vanilla_beanblack_pepper_vinaigrette