Put the sugar in a small nonstick skillet, sprinkle with the lemon juice and water and cook over medium-low heat, stirring, just until the sugar dissolves. Stop stirring and cook, swirling the skillet occasionally, until the mixture turns amber, 4 to 5 minutes. Watch closely--this happens quickly.
Carefully add the heavy cream (the mixture will bubble up) and stir. Stir in the butter until smooth. Remove from the heat and stir in the vanilla and kosher salt. Transfer to a bowl and let cool, at least 30 minutes.
Spread the cooled caramel on the pie. Sprinkle with flaky sea salt before serving.