Combine the milk, 1 cup of heavy cream, sugar and salt in a medium saucepan. Heat the ingredients over medium heat until the sugar has dissolved.
Pour the remaining 1 cup of heavy cream in a medium bowl and set a mesh strainer over the bowl.
Whisk the egg yolks in a small bowl. When the milk mixture is heated through, temper the egg yolks by pouring a ¼ cup of the milk mixture into the eggs, whisking continuously, so the eggs heat up slowly. The eggs can turn into scrambled eggs if you do not whisk continuously.
Pour the tempered eggs into the saucepan with the rest of the milk mixture, and whisk constantly over medium heat. The mixture will be ready when it has thickened and coats the back of a spoon, or the temperature reaches 170°F.
Immediately strain the custard into the prepared cold heavy cream and stir to stop the custard from cooking. Place the bowl of custard over an ice bath and allow the custard to cool completely, about 30 minutes. Cover and refrigerate until ready to churn, 4 hours or overnight.
To make the strawberry puree, place strawberries and sugar into a food processor or blender. Puree until you have a thin sauce. Transfer to a bowl and refrigerate until ready to use.
To make the strawberry sauce, place strawberries, sugar and lemon juice into a medium saucepan. Place over medium heat and bring to a gentle boil. Continue cooking for another 10 minutes, stirring occasionally.
Smash the berries with a potato masher. Continue cooking until the mixture is reduces by half, about 5-8 minutes. The sauce is ready when it is deep red in colour, and thick. Remove it from the heat. Transfer to a bowl, cover and refrigerate until ready to use.
When ready to churn the ice cream, stir in the strawberry puree and sauce. Transfer the ice cream to an ice cream maker and churn according to the manufacture's instructions.
Store the ice cream in an airtight container and place it into the freezer for several hours or until it is ice cream consistency.