Whisk eggs and sugar in a heatproof bowl until well combined. Add the lemon juice and zest, and mix well.
Set up a double boiler: Fill a saucepan with about 1 inch of water and bring it to a simmer. Place the bowl on top of the saucepan, making sure the bottom of the bowl doesn't touch the water.
Cook the mixture, whisking constantly, until the sugar has dissolved completely. Start adding the butter a few pieces at a time, whisking continuously until each batch of butter has melted before adding the next.
Continue to cook and whisk until the mixture thickens enough to coat the back of a spoon. This usually takes about 10-15 minutes.
Once the mixture has thickened, remove the bowl from the heat. If you want a super smooth curd, strain it through a fine-mesh sieve into a bowl to remove the lemon zest and any bits of cooked egg.
Let the lemon curd cool to room temperature, then transfer it to a container and refrigerate until ready to use. It will continue to thicken as it cools.