Combine the rice, herbs, tomatoes, onion, lemon juice, olive oil, salt, pepper, and boiling water in a medium saucepan. Cover and cook over medium heat until the liquid is absorbed and the rice is partially cooked, 10 to 12 minutes. Remove from heat and let cool slightly.
Slice the potatoes into thin rounds and arrange them in an even layer across the bottom of a wide pot. If the grape leaves have a strong brined aroma, soak them in lukewarm water for 10 minutes, then drain well.
Place a grape leaf shiny-side down. Spoon about 1 tablespoon of rice filling near the base, fold in the sides, and roll tightly. Repeat with the remaining leaves and filling.
Arrange the stuffed grape leaves snugly, seam-side down, over the potatoes in tight layers.
Pour the lemon juice, olive oil, and boiling water evenly over the grape leaves. Cover and simmer over medium heat until tender, 50 to 60 minutes. Let rest for 10 minutes before serving.
Serve warm or at room temperature with labneh.