Add the sugar to a medium heavy-bottomed saucepan and heat over medium-low heat, stirring frequently until the sugar has melted and turns golden brown, about 15 minutes. Be patient while the sugar melts. It will clump before it melts then it caramelizes quickly, so keep an eye on it so the sugar doesn’t burn.
Remove the pot from heat and stir in the butter (it will bubble).
Slowly stir in the cream, stirring constantly until completely combined. Let cool completely and use or add to an airtight container and store refrigerated until ready to use.
For the dip and serving:
In the bowl of a stand mixer fitted with the whisk attachment (or in a medium mixing bowl using a whisk) beat the cream cheese and slowly add the confectioner's sugar on low speed until completely combined. Increase the speed to medium and beat until the mixture is light and fluffy, about an additional minute.
Spread the cream cheese mixture on a large platter, serving dish or bowl using a rubber spatula. Spread it so the edges are slightly higher than the middle to help hold the caramel from spilling out. Evenly pour ½ cup (174g) of the caramel sauce over the top.
Squeeze lemon over the top of the apple slices to prevent browning. Serve the caramel dip with the apple slices for dipping.