In a heavy bottomed saucepan over medium heat, melt the butter and add the sliced onions. Stir until onions have softened and are starting to brown, about 3-4 minutes. Season with salt and pepper. Spread onions in an even layer, cover pot, and reduce heat to low. Stir every 5 or so minutes. Continue until onions are nice and brown and caramelized, about 25 minutes. (this may take longer depending on how many onions you use).

Increase heat to medium-high, add the lemon juice to deglaze the pan, and scrape up any brown bits from the bottom. Once all the liquid has absorbed, about 1-2 minutes, turn off heat.

Preheat skillet to medium heat. Butter both sides of bread, lay buttered side down on skillet and cover with 1/4 of cheese, top with half of the caramelized onions, and top with 1/4 more cheese, then buttered bread. Cook until cheese is melted and the outside is golden brown. About 3 to 4 minutes per side. Repeat with second sandwich.