Place the mung beans and rice into a fine mesh strainer and rinse them well under cold running water. Set them aside for now.
Coat the bottom of a medium pot with the oil and place it over medium heat. Give the oil a minute to heat up, then add the ginger, cumin seeds, mustard seeds, fennel seeds, fenugreek seeds, ground cumin, ground turmeric, and black pepper. Cook the spices in the hot oil for about one minute, stirring constantly to prevent them from burning.
Add the mung beans and rice to the pot. Stir everything up well and toast the beans and rice for about one minute, stirring constantly.
Stir in the water. Raise the heat to high and bring it to a boil.
Lower the heat so that the mixture is just cooking at a low simmer, then cover the pot. Let the mixture simmer while covered for about 45 minutes. Check on it every so often and give it a stir. It's done cooking when the bean and rice have broken down and created a creamy mixture (Note 1).
Remove the pot from heat. Stir in the lemon juice, salt, and cilantro.
Divide into bowls. Optionally top with additional cilantro and serve with lemon wedges on the side.