Peel the onions and chop, don't throw the peel away.
Sauté the chopped onion in the fat until soft and translucent (see through). Taste a tiny piece to see if it’s done.
Put the peelings in another saucepan, add half a litre of water and simmer to make stock while the onions are frying
While the onion is frying, prepare the other vegetables. If your carrot and potato are in good condition, there is no need to peel them. Chop into pieces about the size of a large pea. Pile them all into the pan and continue cooking with the onion. Cover the pan and cook on a low heat until all the vegetables are soft and cooked through.This step is not essential and perfectly acceptable soup can be made without it, but the sauté step brings out the sugars of the vegetables and gives you more flavour in the finished soup.
Strain the peelings stock into the soup pot. You can now dispose of the peelings
Once your vegetables are done, add the tomato purée, lentils and the remaining water, no salt yet, it will toughen the lentils. Bring the pan to the boil, now turn down the heat so that the soup is bubbling very gently and put the lid on. Continue simmering for about 20 minutes. The red lentils will melt into the soup in this time.
Add about half a teaspoon of salt and the same of pepper. Stir well and taste. Add more of either if you wish. You can either leave the soup as it is, or whizz it smooth with a stick blender or in a liquidiser.
Now whizz your soup smooth. Add the pepper. Adding it at the end preserves the flavour and heat. Adjust the salt and vinegar to taste. The vinegar really lifts a soup, well worth adding
Serve on it's own, or with some lovely fresh crusty bread
Notes
Priced at Asda January 2020 using MySupermarket.com