Preheat a grill to medium-high. In a bowl, stir the mayo, sour cream, lemon zest and juice and shallot. Stir in the cheese; season with salt and pepper.
Brush steaks with oil and season with salt and pepper. Place the steaks on the grill, cover and cook, turning once, for about 6 minutes for medium-rare.
Transfer the steaks to plates and spoon the sauce on top. Let rest for 5 minutes.