Place the cut orange slices in the compartments of an ice cube tray and cover with orange juice (about 1 3/4 cups). Freeze until firm, at least 6 hours and up to 2 weeks.
Combine lemon juice, simple syrup, and the remaining 4 cups orange juice in a punch bowl and stir to combine. Chill, at least 1/2 hour and up to 8 hours, before serving. Top with the blood orange soda and prepared ice cubes.