1. Bring cream to just under a boil over medium heat in a medium saucepan. Combine sugar, lemon juice, and 3 tablespoons water in a separate, heavy saucepan. Place over medium heat, and, without stirring, bring to a simmer. (If sugar crystals form, dissolve with a wet pastry brush.) Swirl pan to distribute syrup as it starts to color, and cook until amber. Slowly add hot cream, stirring constantly with a wooden spoon. (Mixture may spatter.) Cook 1 minute to dissolve caramel. Remove from heat.
2. Stir in vanilla, kosher salt, and, if desired, rum. Let cool. Store refrigerated in an airtight container up to 5 days; bring to room temperature before using.