Lady apples are tiny—about 2 inches in diameter. Choose ones with sturdy stems to make dipping easier, or use clean twigs as handles. Plus: More Dessert Recipes and Tips
Line a large baking sheet with parchment paper or a silicone mat. If the apple stems aren't sturdy, insert wooden skewers or twigs into the tops.
In a small saucepan, bring the cream just to a boil. Remove from the heat. In a large saucepan, combine 1/2 cup of the sugar with the water and lemon juice. Using a wet pastry brush, wash down the side of the saucepan. Bring to a simmer over moderate heat without stirring and cook until the syrup begins to color around the edges, about 4 minutes. Swirl the pan carefully, then simmer until the caramel turns a light amber color, 2 to 3 minutes longer. Remove from the heat. Using a long-handled wooden spoon, carefully stir in the hot heavy cream.
Return the caramel to the heat and stir in the corn syrup, salt and the remaining 3/4 cup sugar. Add the butter and bring the caramel to a boil over moderately high heat. Wash down the side of the saucepan with a wet pastry brush. Insert a candy thermometer in the caramel and cook it over moderate heat until the thermometer registers 242°, 6 to 7 minutes. Set the saucepan on a wire rack and stir in the vanilla. Let the caramel stand for 5 minutes to cool slightly.
Working quickly, dip the lady apples into the caramel, letting any excess drip back into the pan. Set the apples on the prepared baking sheet. If the caramel becomes too thick, gently rewarm it over low heat. Let the caramel apples cool for 1 hour before serving.
The caramel apples can be made up to 4 hours ahead.