Place sugar and cornflour into a heavy based, medium sized saucepan. Whisk in milk and cream then whisk over medium heat until gelato base thickens and begins to bubble, about 5 minutes. Cool quickly over ice then add lemon juice and vanilla.
Puree strawberries in food processor. Strain into gelato base - leave in a few seeds for that authentic strawberry texture. Chill 3 hours. Process in ice cream maker according to manufacturer's instructions. Transfer to a chilled container, cover tightly with a lid or plastic wrap then place in the freezer to firm up completely.