Sprinkle 2 tbsp of sugar (or erythritol, for sugar-free version) on frozen strawberries and set aside.
If using fresh strawberries, wash and hull them first cut in half.
Put cream and milk into a heavy-based saucepan and add vanilla bean, split down the middle lengthwise.
Bring the mixture to nearly boiling and take it off the heat and leave to let the vanilla infuse for 20 minutes.
Combine egg yolks and sugar (or erythritol) in a large mixing bowl and whisk by hand or using a mixer until thick and very light in color.
Take vanilla bean out of the saucepan and pour the warm milk and cream mixture over the yolks slowly while whisking.
Then return the mixture into the the same saucepan using a strainer (not the fine mesh or it will catch some of the super tiny vanilla caviar, it happened to me and I had to scoop them out and return in the custard)
Put the saucepan with the custard back on the stove over medium heat and stir until the mixture thickens (it should coat the back of the spoon) then take off the heat and pour into a clean bowl to cool.
Puree the strawberries in a blender or food processor and fold into the cooled custard until fully incorporated then add the lemon juice
Pour into a freezer-proof container and put in the freezer.
Whip every hour for 3 hours as it freezes using ether a whisk or electric beater to get rid of any ice crystals that form and that makes the ice cream crunchy instead of smooth.
Alternately, if you have an ice-cream maker, just pour the custard into it and put it into the freezer.