Pulse blackberries in a food processor until smooth. Pour blackberry paste through a fine mesh sieve to strain pulp. Discard pulp.
Place blackberry juice into a small pot and combine with lemon juice and sugar over medium heat. Stirring frequently, reduce blackberry juice for 5-7 minutes until thickened. Set aside and let cool.
Next, beat heavy cream on medium speed until medium peaks form, about 5 minutes.
Reduce speed and gently pour in sweetened condensed milk for an additional one minute of mixing.
Using a spatula, fold vanilla extract and vanilla bean pods into cream.
Stir in blackberry paste and pour into a freezer safe container. Cover and let chill in the freezer for at least 5 hours before serving.