Bring the water, brown sugar, white sugar, ginger, peppercorns, allspice, and cinnamon sticks to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer 30 minutes. Strain the liquid into a heatproof container, and discard the spices. Refrigerate overnight to cool.
Pour the chilled spice mixture into a large punchbowl. Stir in the vodka, rum, orange juice, pineapple juice, and crushed ice. Garnish with lemon slices to serve.