In a bowl, mix the mayonnaise, minced garlic, and lemon juice. Set aside in the refrigerator.
Preheat the grill for high heat.
Brush vegetables with olive oil on each side. Brush grate with oil. Place bell peppers and zucchini closest to the middle of the grill, and set onion and squash pieces around them. Cook for about 3 minutes, turn, and cook for another 3 minutes. The peppers may take a bit longer. Remove from grill, and set aside.
Spread some of the mayonnaise mixture on the cut sides of the bread, and sprinkle each one with feta cheese. Place on the grill cheese side up, and cover with lid for 2 to 3 minutes. This will warm the bread, and slightly melt the cheese. Watch carefully so the bottoms don't burn. Remove from grill, and layer with the vegetables. Enjoy as open faced grilled sandwiches.