In a medium heavy saucepan, combine 3/4 cup of the sugar with the water and lemon juice and bring to a simmer over low heat, stirring occasionally until the sugar dissolves. Bring to a boil and cook without stirring, swirling the pan occasionally, until the syrup caramelizes and turns a deep golden color, 7 to 10 minutes. Very carefully pour the mixture into 6 (1-cup) ramekins and swirl to evenly coat the bottoms. Set aside.

Preheat the oven to 350 degrees F.

In a medium saucepan, bring the cream and milk to a simmer. Remove from the heat.

In a medium bowl, whisk together the eggs and remaining 1/2 cup sugar until frothy and lemon colored, 2 to 3 minutes. Whisking constantly, slowly add the hot cream mixture to the eggs. Whisk in the rum. Strain through a fine mesh strainer into a large glass measuring cup or bowl, and divide among the ramekins.

Place the ramekins in a large roasting pan and place on the middle rack of the oven. Carefully fill the roasting pan with hot water to come halfway up the sides of the ramekins. Bake until the custards are just set and a knife inserted into the center comes out clean, about 30 minutes.

Carefully remove from the oven. Transfer the custards to a wire rack to cool, then refrigerate and chill completely before serving, 4 hours or overnight.

To serve, run a thin sharp knife around the custards to loosen and invert onto dessert plates. Shake gently to release onto the plates. Garnish with the caramelized pineapple and pink grapefruit and serve.