In a bowl, mix chopped strawberries with 1/4 cup of sugar and lemon juice. Let sit for 30 minutes, then puree half the mixture.
In a saucepan, heat cream and milk until steaming but not boiling.
In a separate bowl, whisk egg yolks with remaining 3/4 cup sugar until pale and creamy.
Slowly pour the hot cream mixture into the egg mixture, whisking constantly.
Return the mixture to the saucepan and cook over low heat, stirring constantly, until it thickens enough to coat the back of a spoon.
Remove from heat and stir in vanilla extract and salt.
Strain the mixture into a clean bowl and let it cool to room temperature.
Stir in the pureed and chopped strawberries.
Refrigerate the mixture for at least 4 hours or overnight.
Churn the chilled mixture in an ice cream maker according to manufacturer's instructions, usually 20-30 minutes.
Transfer to an airtight container and freeze for at least 4 hours before serving.