Bring 2 tablespoons water to a boil in a small saucepan. Reduce heat; add 6 tablespoons butter, a little at a time, whisking until butter is completely melted.

Whisk together flour, sugar, and salt in a medium bowl. In a separate bowl, whisk together milk, vanilla, and eggs. Gradually add milk mixture to flour mixture, whisking until smooth. Whisk in butter mixture. Pour batter through a fine sieve into a bowl; discard lumps. Transfer batter to an airtight container; refrigerate at least 2 hours (or overnight).

Preheat oven to 200 degrees. Lightly coat a 6-to 7-inch crepe pan or nonstick skillet with melted butter. Heat over medium heat until just starting to smoke. Remove pan from heat; pour 2 to 3 tablespoons batter (depending on size of pan) in center. Swirl to cover bottom. Reduce heat to medium-low; return pan to heat. Cook until edges of crepe turn golden and center is dry, about 45 seconds. Flip crepe; cook until underside is brown in spots, about 45 seconds more.

Slide crepe onto an ovenproof plate; cover with foil, and transfer to oven. Repeat process with remaining batter, coating pan with more butter as needed.

Fold each crepe into quarters to form a triangle. Arrange 3 crepes on each plate; drizzle with lemon-caramel sauce and garnish with candied lemon slices.