Bring water to a boil in a large pot. Cook lentils in boiling water until beginning to soften, 8 to 10 minutes. Add chard; continue cooking until wilted, about 5 minutes.
Add potatoes to the boiling water, reduce heat to medium-low, cover the pot, and cook until the potatoes are completely cooked, about 12 minutes.
Mix lemon juice, crushed garlic, and salt together in a bowl; add to the pot. Continue to cook at a simmer another 5 minutes. Stir olive oil into the mixture. Increase heat to high and cook another 1 to 2 minutes.