Preheat oven to 400 degrees F. Combine lemon juice and Worcestershire sauce, and sprinkle on the fish pieces. Salt and pepper the fish, then dredge lightly in flour. Dip the fish in eggs, then coat generously with the grated cheese.
In a heavy skillet, saute the fish in a mixture of butter and oil over medium heat for 3 to 4 minutes to brown.Turn and brown the other side.
Place the skillet in the oven for 4 to 5 minutes to heat through. Serve immediately.