In a 3qt (or larger) pot with sloped sides, whisk together the sugar, water, and lemon juice until the sugar has dissolved.
Use a pastry brush, dipped in water to brush down the sides of the pot. This will remove any undissolved sugar crystals, which will cause your sugar to crystallize.
Add a candy thermometer (if using one) to the pot, then bring the mixture to a simmer over medium heat.
Slowly cook the sugar, without stirring, until the mixture reaches 310°F, or until it appears dark amber in color, this may take anywhere from 10-15 minutes.
While you're waiting for your sugar to reach the caramel stage, heat the heavy cream in the microwave (or on the stovetop) until it's steaming- about 30 seconds to a minute. Stir in the vanilla bean paste to infuse the cream with vanilla flavor.
Fold and set a kitchen towel on the counter to set the hot pot on. Once your caramel has reached the proper temperature, remove it from the stove, and place it on the folded towel.
Carefully pour in the heated, vanilla-infused cream, whisking constantly (try to keep your hand out of the path of the steam). The sauce will spatter and steam when the cream is added. The caramel may clump up after you've added the cream, that's normal, just continue stirring with the whisk.
Whisk in the sea salt (or kosher salt) and the butter, and whisk until the butter is melted and the caramel is completely smooth.
Allow the sauce to cool to room temperature. Serve once it's cool, or transfer to a clean jar and store, refrigerated, up to two weeks.