Combine peaches, lemon juice, salt, and cinnamon: In a medium bowl, toss together peaches, lemon juice, salt, and cinnamon; set aside.
Melt butter and sugar; add peach mixture and cook: Melt butter and sugar in a large skillet over medium-high heat. Add peach mixture and cook, stirring occasionally, until caramelized, about 5 minutes.
Add bourbon or rum, if using: If using bourbon or rum, add to skillet, and cook until reduced, about 1 minute.
Serve: Serve immediately over ice cream, if desired.
