Brush the flank steak on both sides with the mustard. Put the steak in a sturdy resealable plastic bag and add the wine. Seal the bag, pressing out any air, and refrigerate overnight. Drain the steak, pat dry and bring to room temperature before grilling.
Meanwhile, in a small saucepan, combine the olive oil and garlic and cook over low heat until the garlic is golden and soft, about 15 minutes. Using a slotted spoon, transfer the garlic to a small bowl; reserve the garlic oil. Add the thyme to the garlic and mash to a paste. Stir in the mayonnaise and lemon juice and season with salt and pepper.
Light a charcoal grill or preheat a cast iron grill pan. Brush the steak with the reserved garlic oil, season liberally with salt and pepper and grill over moderate heat for about 15 minutes, turning once, for medium-rare meat. Transfer the steak to a cutting board to rest for 5 minutes. Thinly slice the meat across the grain on the diagonal.
Spread the garlic mayonnaise on the rolls and top with the flank steak, cheese and lettuce. Cut the sandwiches in half and serve.