It is a myth that lentils do not contain all the essential amino acids. Lentils contain all 9 amino acids, and are technically a complete protein by themselves. However, they are extremely low in the amino acid methionine. The amount of methionine in them being so low makes it the limiting factor as a protein source. Once all the available methionine is used up, the rest of the amino acids are no longer bioavailable.
So, no, technically lentils by themselves would not be sufficient as a sole source of protein. However, if you combine them with a secondary source of methionine, from whole grain brown rice as an example, they would have sufficient methionine to be used as a significant protein source.
With all that said, I don't know why anyone would want to limit their protein intake to strictly legumes. I like beans and all, but they eventually get old. Especially in the amounts that you would have to eat them as a sole protein source in your diet. Eggs are cheap, and are the most bioavailable protein you can consume.
So, yes you technically can use lentils as your sole source of protein, as long as mix them with something that will provide more methionine. I just don't know why you would want to. Almost everything gets old if you eat a lot of it for a long period of time. One of the most important aspects of a diet plan is it's sustainability. If a food becomes unappetizing and you find yourself unable to consume it in large enough quantities for extended periods, then it isn't doing anything positive for you.