Place the cubed watermelon in a blender. Blend until completely smooth, about 30 seconds.

Pour the puree through a fine-mesh strainer set over a bowl. Press on the solids with a spatula to extract as much juice as possible. You should have about 1 1/2 cups of juice. Discard the pulp.

In a small saucepan, combine the watermelon juice and sugar. Warm over medium heat, stirring occasionally, until the sugar dissolves completely. Do not let it boil. Remove from heat and stir in the lemon juice. Let cool to room temperature, then refrigerate until completely cold, about 1 hour.

In a large mixing bowl, pour the cold heavy cream. Using an electric hand mixer or stand mixer with the whisk attachment, beat the cream on medium-high speed until stiff peaks form. When you lift the beaters, the cream should stand up straight without drooping. Be careful not to overbeat or it will turn into butter.

Gently fold the chilled watermelon syrup into the whipped cream. Use a spatula and a gentle hand, cutting through the cream and folding until just combined. The mixture should be a uniform pale pink with no streaks.

Pour the mixture into a 9x5 inch loaf pan. Smooth the top with a spatula. Cover tightly with plastic wrap, pressing the wrap directly onto the surface to prevent ice crystals.

Freeze for at least 6 hours, or overnight, until firm. Let sit at room temperature for 5-10 minutes before scooping for easier serving.