Heat the grill or grill pan over medium-high heat.
Grate the garlic into a medium bowl and pour the lemon juice over. Let stand about 2 minutes. Whisk in the yogurt, 2 tablespoons water and 1/2 teaspoon salt.
Put the chickpeas in a large bowl. Stir in 1/4 cup of the yogurt sauce and set aside.
Brush the eggplant slices generously with olive oil on one side and season with salt. Grill oiled-side down until charred, rotating once to char more of the surface, 2 minutes total. Brush oil on the top, sprinkle with salt, flip, and grill until charred and very tender, another 1 to 2 minutes. Transfer the eggplant to a cutting board, chop roughly, and then stir gently into the chickpea mixture. Taste the mixture and season with salt, if needed.
To make the wraps, spread 2 tablespoons of the yogurt sauce on one of the tortillas. Sprinkle with 1 teaspoon of the oregano. Form about 1 scant cup of the chickpea mixture into a log across the wrap about 3 inches from the bottom, leaving a 1-inch border on each side. Top with some chopped tomatoes and a little salt, then add some cucumber and lettuce. Fold the sides of the wrap over the ends of the chickpea mixture, then roll up tightly from the bottom. Repeat for the remaining tortillas and filling. Cut each in half on the bias, and serve.
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