Over medium-high heat (do not bring it to boil), place the shallot and lemon juice in a sauce pan. Cook and stir until the lemon juice has reduced by half.
Once the lemon juice has reduced to half, remove from the heat, the pan will still be warm, and begin adding two tablespoon of butter at a time and stir constantly until incorporated. Make sure the pan/sauce stays warm, and if it needs to return to the stovetop, do so to keep the sauce warm, but do not bring to boil or it will likely break.
If the sauce breaks, you can add one ice cube and stir until it retains the consistency you want while stirring over medium-high heat. You can also use a touch of heavy cream, but the ice cube would be my recommendation. You can only do this once, but it most definitely can work the first time.
Stir in the remaining butter until fully incorporated. You can keep the sauce warm if you are not serving it immediately, by placing it in a warm water bath. In a large casserole dish, or larger than your sauce pan, place hot tap water - about 1-2 inches. Place the sauce pan, with the sauce into the casserole dish with the water and set aside until you wish to serve it.