Make the ginger ale: Combine the ginger and water in a small saucepan. Bring to a boil over high heat, then reduce the heat to low and simmer, partially covered, for 35–40 minutes, or until the ginger is soft.
Strain out the ginger, then return the liquid to the saucepan. Add the sugar and cook, stirring, over low heat, until the sugar is dissolved. Stir in the lime juice and remove the pot from the heat. Let cool to room temperature and then transfer to a jar with a lid and refrigerate for 1 hour, or until ready to use.
In a large bottle with a cap, combine the ginger syrup and seltzer water. You should have about 4½ cups. Use immediately or refrigerate for up to 24 hours.
To make the cocktail, add the Crown Royal Salted Caramel, Crown Royal Regal Apple, and lemon juice to a glass. Add ice to almost fill the glass and stir a few times to combine. Top with 4 ounces of ginger ale and garnish with the caramel-dipped apple slice.