Microwave lime in a small bowl to release essential oils and set aside until it is just cool enough to handle.
Rinse beef to remove any blood residue and pat dry with paper toweling. Rub with salt and pepper and set aside briefly. Combine shallots, garlic, thyme, parsley, sage and olive oil to form a smooth paste. Rub into beef and let sit for a minimum of 2 hours.
Preheat oven to 350 degrees F. Heat oil in a large saute pan with an oven safe handle, and sear beef on all sides. Roast in oven until the beef reaches an internal temperature of 125 degrees F, about 20 to 25 minutes, so when you pull it out it will reach 145 degrees F for medium doneness during the carryover cooking while it is resting. (You will be using the pan juices for the lentils, so do not discard them.)
While the beef is roasting, rinse lentils in a colander and examine to make sure there are is no foreign material (such as pebbles). Transfer to a saucepot with just enough water to cover, and bring to a boil. Reduce and simmer for about 20 minutes until lentils are re-hydrated and water is absorbed, then remove from heat.
While lentils are cooking, heat olive oil in a large skillet over medium heat, and saute white onion until translucent. Add 2 tablespoons butter to the saute pan and when it melts, add shiitake, crimini, and portobello mushrooms to the onion pan along with sage and thyme. Cook mushrooms until they begin to soften and to give up their juices. Stir sauteed onion- mushroom-herb mixture into pot of lentils along with demi-glace. Lower heat and cook for a few minutes to integrate flavors, but do not allow lentils to get mushy. Remove from heat and keep in a warm place.
Remove beef from oven and transfer to a utility platter to let rest. Strain pan juices from beef into lentil mixture and stir to combine. Keep covered and warm.
Sliced rested beef into thin slices. Stir diced tomato into lentils. Spoon some lentil/mushroom mixture into the center of serving dish and top with beef. Garnish with chopped parsley.