Bake-sale Lemon Meringue Pie

• 15 room
• 5 eggs (separated)
• 1 refrigerated pie crust
• 1/4 stick
• 350 ml water
• 250 gr sugar
• 120 ml lemon juice (fresh)
• 65 gr sugar
• 50 gr cornstarch
• 18 gr butter (unsalted)