Depending on the cut of beef liver, the membrane may need to be removed if it's still attached. You can do this easily by using a paring knife to cut through the membrane and peel off the membrane.
Gently rinse liver in water. Then, place liver in a shallow bowl and cover with milk. Let liver soak in milk for at least 30-minutes and up to 2 hours. This will remove the bitter flavor. Remove from milk, rinse in cold water, and pat dry with paper towels.*
Thinly slice liver into 1/2-3/4″ thick slices, and slice yellow onion into rings.
Melt butter in a large skillet over medium heat. Add onion rings; cook and stir in butter until tender and soft, about 3 to 5 minutes. The onions will be soft, but not caramelized. Remove cooked, buttered onions from skillet and transfer to a plate.
Add liver slices to skillet, and sprinkle with salt and pepper. Increase heat to medium-high heat, and cook liver until browned on one side, approximately 2-3 minutes. Flip and cook on the other side until browned.
Add onions back to skillet with liver. Reduce heat to medium. Cook until onions are heated and liver is slightly pink in center, approximately 3 minutes. Remove liver and onions from skillet and transfer from a plate.
If desired, mix water, lemon juice and Worcestershire sauce. Heat liquid sauce in the same skillet and heat through. Pour over the liver and onions
Serve immediately. Enjoy!
Notes
*If dairy-free, soak liver in water with two tablespoons of apple cider vinegar or lemon juice.