Zest 2 of the lemons using a zester or grater. Cut all three lemons in half and juice to measure 1/2 cup.
Place the diced butter in a mixing bowl and set aside.
In a small saucepan combine lemon zest, lemon juice, sugar, and eggs.
Whisk over medium heat until it starts to simmer and thicken. This does take some time, so be patient.
When mixture has started to simmer and thicken, remove from heat and strain into the butter.
Whip with whisk until smooth (or use a immersion blender) about two minutes.
Spread filling into the cooled tart shell and chill
Optional Candied Lemon Slices
For candied lemon slices, slice the 4th lemon into very thin slices. In a saucepan bring 1/2 cup granulated sugar and 3/4 cup water to a boil over medium heat. Add the lemon slices, lower heat and continue to cook for approximately 10 minutes, until peel is almost translucent. Remove from heat and allow to cool in the liquid.
After the tart has chilled for at least an hour, remove candied lemon slices from the liquid and drain on paper towels. Arrange over tart.
Apricot Glaze
Heat apricot jam over low heat until melted. Brush over the surface of the tart and return to refrigerator until ready to serve.