Remove the rind from the watermelon and discard. Place the watermelon flesh in a food processor and process until smooth. Pass the puree through a sieve and discard any solids. Add the vodka to the watermelon puree and refrigerate for 2 hours.
Pour watermelon vodka into tall glasses until 1/4 full, then top up with soda water or lemonade. Add lots of crushed ice and garnish with lemon slices.