Combine sugar and water in a medium saucepan. Bring to a boil over medium-high heat, stirring to dissolve the sugar. Reduce heat to low and simmer for 5 minutes. Remove from heat and let cool to room temperature, about 45 minutes. Cover and refrigerate until chilled, about 1 hour.

Place watermelon and lime juice in a food processor; process until smooth. Set a sieve over a large bowl and press the puree through to remove tiny seeds. Whisk in the sugar syrup.

Pour the watermelon mixture into a shallow metal pan and freeze until ice crystals form around the edges, about 30 minutes. Stir the ice crystals into the centre of the pan and return to the freezer; repeat every 20 minutes until all the liquid is frozen.

Serve immediately or transfer to a storage container and let harden in the freezer for 1 to 1 1/2 hours.

To serve: place in chilled dishes and drizzle with olive oil and sprinkle with sea salt flakes.