Heat the oven to 375°F. Lightly grease a 12-cup muffin tin.
Heat the olive oil in a large skillet over medium heat. Add the mushrooms and onion. Cook for 6 to 8 minutes, stirring often, until softened and most of the mushroom liquid has evaporated. Set aside about one-third of the mixture for the gravy and let the rest cool slightly.
In a large bowl, combine the lentils, ground turkey, egg, breadcrumbs, Worcestershire sauce, dried thyme, salt, black pepper, and the larger portion of the cooled mushroom and onion mixture. Mix gently until just combined.
Divide the mixture among 8 cups of the prepared muffin tin, filling each cup evenly. Bake for 22 to 26 minutes, until the centers reach 165°F.
While the muffins bake, return the reserved mushroom mixture to the skillet over medium heat. Stir in the tomato paste and flour, and cook for 1 minute.
Gradually whisk in the chicken broth. Bring the gravy to a gentle simmer and cook for 4 to 6 minutes, stirring, until thickened. Spoon the mushroom gravy over the turkey meatloaf muffins to serve.