First of all, let me explain you what the matter with lentils is. Basically, we need to start from raw lentils (any type will be fine), the dry ones, and cook them for a very short time, halfway through. Canned lentils won't do.
Take the lentils (about 2 cups), rinse in cold water and cook with plenty of water in a pressure cooker.
Cook the lentils in the pressure cooker for 5 minutes, no longer and no shorter than that: remember that we aim to having our lentils cooked only halfway.
If you don't have a pressure cooker, just cook the lentils in a normal pot but not too long, they need to be firm, somehow still crunchy, not mushy.
Drain the lentils and mash them with a meat grinder or a food processor until you have a rough mixture.
Mix the lentils with the raw egg, add the remaining ingredients just as you would do if you were making meatballs, to obtain a compound that does not stick to your hands.
Heat a little oil or butter in a frying pan and prepare the burger pattie.
Cook the burger on both sides for about 5 minutes.