Bring garlic, tomatoes, onion, tchicha, tomato paste, khlii (if using), pepper, 6 cups water, and 1 tablespoon salt to a boil in a large saucepan over medium-high. Reduce heat to medium; simmer, uncovered, stirring occasionally, until tchicha is tender, about 30 minutes. As soup cooks and thickens, stir in remaining 2 cups water, as needed, to thin to a creamy consistency.

Stir in thyme and remaining 1 teaspoon salt; season with additional salt to taste, if needed. Simmer until very fragrant, about 5 minutes. Remove from heat, and stir in lemon juice. Serve with lemon wedges.