Combine the rapberries, the lemon juice, and 1/3 cup sugar in a bowl. Leave on the counter for two hours. The raspberries will release their juices and absorb some of the sugar. This will lower the freezing point of the raspberries so that they do not turn into rocks in your ice cream!

In a separate bowl, mix 1 cup whole milk with the remaining 2/3 cup sugar and stir until the sugar is dissolved.

Add the heavy cream and vanilla. Pour in the liquid from the bowl with the raspberries, reserving the raspberries. Mix well. (I poured the raspberries and their juices over a strainer to separate the juice. I pressed the raspberries down a little to release more juice and to break up the raspberries a bit).

Pour the milk, cream, and raspberry juice mixture into your ice cream maker and follow the manufacturer's directions.

When ice cream has reached soft-serve consistency, add the raspberries. Let the ice cream maker run another minute or two to distribute the raspberries throughout the ice cream.

Transfer to an airtight container in layers, drizzling each layer with the melted chocolate.

Store in the freezer for several hours or overnight.