Place a pot with water over medium heat. Once it starts to boil reduce the heat until you see only a slight simmer and place a bowl on top. Make sure that the base isn't touching the water in the pot. This is a bain-marie or double boiler.
Add the lime juice, lime zest and sugar onto the bowl and let it sit there until the sugar is completely dissolved.
Add the eggs off the heat and quickly whisk them in. Place the bowl back onto the bain-marie and whisk constantly until the curd cooks. It's ready when you can see it's more gelatinous. Also if you draw a shape with the mix on its surface it will stay there. This will take 15-25min. You want to avoid over cooking the curd or it could curdle.
Remove from the heat and transfer to another bowl through a sieve or colander. The colander will catch large pieces of zest and also any egg that cooked funny. Changing it to another bowl will also stop the cooking process. Add the butter and mix until fully melted and incorporated.
Let cool completely to room temperature before filling the tart. Then fill the tart and spread it using a spatula. Place in the fridge overnight to set.