Add tomato paste, oregano, red pepper flakes, and chopped walnuts. Cook for another minute or two while the tomato paste browns a bit. Stir in the balsamic vinegar for one minute.
Add veggie broth, dry lentils, and canned tomatoes. Stir to incorporate.
Bring up to a boil, then lower the heat to a gentle simmer. Cover, stirring occasionally while the lentils soften (about 20 minutes).
Remove the lid, stir in ½ cup dairy-free milk or ¼ cup heavy cream. Continue to simmer for another 20+ minutes while the flavors develop and the sauce reduces. Stir occasionally.
Taste and adjust salt, balsamic, and red pepper flakes as needed. If the sauce is too acidic, add a teaspoon of maple syrup.