Which food group do beans and lentils belong to?

Legumes, and their importance is not really nutritional. Legumes host bacteria in nodules on their roots that convert nitrogen gas from the air into a form plants can use - the trick almost nothing else can do, and the reason a legume leaves soil richer than it found it.

That single fact organised agriculture for two thousand years. Crop rotations pairing cereals with beans, peas or clover kept land productive without any understanding of why, and the collapse of that system was the fertility crisis of the nineteenth century, solved only by industrial nitrogen fixation after 1913. Roughly half the nitrogen in a modern human body has been through a factory rather than a root nodule.

Nutritionally they pair with grains in a way that appears independently in cuisines that never met: beans and maize in Mesoamerica, lentils and rice across South Asia, chickpeas and wheat in the Middle East, soy and rice in East Asia. Grains are short of the amino acid lysine and legumes have plenty; legumes are short of methionine and grains have plenty. Nobody worked this out - the combinations were simply the ones on which people stayed healthy.