In a medium saucepan, cover the lentils with 1 inch of water. Add the turmeric and bring to a boil. Simmer over moderately low heat until the lentils are tender and most of the liquid has evaporated, about 25 minutes.
In a small skillet, melt the butter. Add the cumin and mustard seeds and cook over moderately high heat until fragrant, about 1 minute. Add the onion, garlic, chiles and ginger and season with salt and pepper. Cook over moderate heat, stirring occasionally, until the onion and garlic are browned, about 5 minutes. Remove from the heat and add 3 tablespoons of lemon juice, stirring to scrape up the browned bits from the bottom of the skillet.
Add the onion mixture to the lentils along with the bread crumbs and cayenne and season with salt and pepper. Stir in the eggs until blended. Form the lentil mixture into 1/4 cup patties, 2 inches wide and 1/3 inch thick. Let the patties stand for 10 minutes.
In a bowl, stir the yogurt with the remaining 3 tablespoons of lemon juice. Stir in the cucumbers and cilantro and season the raita with salt and pepper.
Light a grill. Brush the lentil patties on both sides with oil and grill over moderate heat until grill marks form and the patties are heated through, about 3 minutes per side. Serve the lentil patties wrapped in the lettuce leaves and pass the raita at the table.
The lentil sliders and raita can be refrigerated overnight. Bring the sliders to room temperature before grilling.