To make the lemon ice, tip the lemons into a blender with the sugar and 500ml/18fl oz of water. Blitz everything for a minute or two until the lemon is chopped to a pulp.
Strain the juice into a shallowish freezer container, pressing down on the lemon pulp with the back of a large spoon to release as much flavour as possible. Discard the pulp.
Reserve two tablespoons of the juice in a medium bowl. Cover the rest with cling film and put in the freezer for four hours or until firm. There’s no need to wash the blender yet.
When the juice is frozen, break it into chunks and tip it back into the blender. Blitz until it’s a smooth sorbet consistency. Tip it back into the freezer container and return it to the freezer for another 30 minutes to firm up.
While the ice is freezing, hull and slice the strawberries, roughly chop the mint, then toss them together in the reserved lemon juice.
When the ice is scoopable, spoon it into bowls and top with the strawberries.