From what I understand Lentil needs Rice for the maximum benefit of its high protein quantity, of course that will then increase the carbs. What is the minimum ratio of rice to lentils to maximize protein to carb ratio while making the protein complete?
Incomplete vs. Complete Protein Complete proteins contain all nine essential amino acids. The main sources of complete proteins are from animal based food, such as meat, seafood, eggs and dairy. Soy and quinoa are also complete proteins. Although incomplete proteins sounds like they are lacking and not as nutritious, they just need to be paired with another type of protein. For instance, adding peanut butter to bread creates a complete protein. According to Columbia University, the proteins do not need to be eaten together to receive the health benefits but any time within 24 hours will suffice.
Lentils and Protein Lentils are rich in amino acids and high in protein. However, regular lentils are lacking in two essential amino acids. Because lentils do not have enough of these nutrients, the healthy legumes are an incomplete protein. However, lentils can be sprouted which changes their nutritional components. Sprouted lentils have an increase in all nine amino acids, although the exact increase is variable. To sprout your lentils, soak the seeds in cool water for eight to 12 hours. Rinse the lentils and store in a jar in a cool place for a few days, rinsing every eight hours.
Source: http://www.livestrong.com/article/527529-myth-of-lentils-as-an-incomplete-protein/
Grains Grains, such as rice, oats, wheat, rye and corn, can act as complementary proteins for legumes such as lentils. They contain the cysteine and methionine that lentils lack, and lentils provide the lysine that grains do not contain enough of. Whole grains are a more nutritious option than refined grains. Legumes and grains are one of the most common pairings for complementary protein. Indian daal with rice is an example of a lentil and grain dish.
Source: http://healthyeating.sfgate.com/foods-mixed-lentils-provide-complete-source-amino-acids-1195.html