Combine berries, sugar, and lemon juice in a small saucepan. Cook over medium heat, mashing gently with a fork or potato masher, until berries break down and the sauce thickens slightly (about 5-7 minutes).

Remove from heat and let cool completely to room temperature. This is crucial; warm berries will melt the ice cream base.

In a large mixing bowl, using an electric mixer, whip the cold heavy cream on medium-high speed until stiff peaks form (about 3-5 minutes). Be careful not to over-whip, which can result in a grainy texture.

In a separate bowl, whisk together the cold sweetened condensed milk, vanilla extract, and pinch of salt until well combined.

Gently fold about one-third of the whipped cream into the condensed milk mixture to lighten it. Then, gently fold in the remaining whipped cream until no streaks remain. Be careful not to deflate the cream.

Pour half of the ice cream base into a 9x5 inch loaf pan or other freezer-safe container.

Spoon half of the cooled berry swirl over the base. Using a knife or skewer, gently swirl the berry mixture into the ice cream base, being careful not to overmix.

Pour the remaining ice cream base over the top.

Spoon the rest of the berry swirl on top and repeat the swirling process.

Cover the loaf pan tightly with plastic wrap or aluminum foil, pressing the wrap directly onto the surface of the ice cream to prevent ice crystals. Freeze for at least 6 hours, or preferably overnight, until firm.