Separate the egg whites from the yolks. Set aside the egg whites for another purpose and place the egg yolks in the bowl.
Pour the fresh lemon juice into the bowl with the egg yolks and whisk them well. Add mustard and stir to combine.
Slowly, a few drops at a time, pour the oil into the bowl while whisking constantly. Once the mayonnaise has started to thicken, pour the oil in a slow and steady stream. If the oil starts to build up at all, stop pouring and whisk the mayonnaise briskly until the oil has incorporated.
If the mayonnaise starts looking too thick, add enough water to thin it to the consistency you like. Add about a teaspoon of water at a time.
Once all the oil has been mixed in, the mayonnaise should be thick and fluffy, with your whisk forming ribbons through the mixture.
Season it carefully with fine grain sea salt. Add a small splash of water if you would like a thinner mayonnaise.