In a small bowl, whisk together mayonnaise, ketchup, salt, pepper, Worcestershire sauce, and lemon juice to make the Russian dressing.
Butter one side of each slice of bread.
Spread a spoonful, or desired amount, of Russian dressing over the other side of each piece of bread.
For each sandwich, layer one piece of bread, 1 slice of cheese, several slices of corned beef, ½ cup sauerkraut, another slice of cheese, and topped with a second piece of bread. The dressing sides of the bread slices should be facing in, while the buttered sides of the bread should be facing out. Repeat to make 4 sandwiches.
Heat a non-stick skillet over medium heat. Place each sandwich into the skillet, you may cook more than one at a time if they fit in the skillet. Cook on the first side until the bread has browned and the cheese begins to melt. Carefully flip the sandwich and cook on the other side.
Cook until both sides are browned, the cheese is all melted, and the sandwich is heated through. You may need to lower the heat to make sure the cheese melts and the sandwich heats through without the bread burning.