Create an ice float by freezing water in a plastic container (choose a size that will make a shape to fit comfortably in your punch bowl) for at least 6 hours or overnight.
Combine the pomegranate juice, lemonade and rum in a large punch bowl and stir well to incorporate. When ready to serve, add the large ice float, stir well and then chill for at least 15 minutes. Garnish with the berries and lemon wheels. Serve over ice in coupe or punch glasses.
If not using an ice float, chill the drink for at least 2 hours and serve over ice.