Heat the butter, corn syrup, and 1⁄4 cup of water in a medium saucepan over medium-low heat, stirring constantly, until the butter has melted.
Stir in the granulated sugar and the brown sugar and scrape down sides of pan with a rubber spatula. Bring the mixture to a boil over medium heat (don’t stir at this point). Cook until the mixture is light brown and a candy thermometer inserted in sauce reads 245°F, 6 to 8 minutes.
Remove from the heat. Carefully pour in the heavy cream, rum, vanilla extract, salt, and lemon juice. Stir to mix well. Cool to room temperature before using.
To assemble the sundae:
Place the 2 scoops of ice cream in a bowl.
Scatter over the banana slices and pistachios, drizzle with the butterscotch sauce, and serve.