Freeze your ice cream maker bowl until solid (per manufacturer) and line a 9Ă—5-inch loaf pan with plastic wrap; chill the pan.
Measure 1 cup granulated sugar. In a bowl, toss the fresh strawberries with 2 tbsp of the measured sugar and the lemon juice; let sit until juicy, 20–30 minutes, then puree until smooth and chill.
In a medium saucepan, combine the whole milk, heavy cream, 1/2 cup of the remaining sugar, and the fine sea salt; heat over medium until steaming with small bubbles at the edges, 3–5 minutes.
In a separate bowl, whisk the large egg yolks with 1/4 cup of the remaining sugar until thick and pale, 1–2 minutes. Slowly whisk in about 1 cup of the hot dairy, then return the mixture to the saucepan.
Cook over low heat, stirring constantly with a heatproof spatula, until the custard coats the back of the spoon or reaches 175–180°F, 5–7 minutes. Strain through a fine-mesh sieve into a large bowl.
Divide the warm custard evenly among three bowls. Into one bowl, whisk the Dutch-process cocoa powder and the bittersweet chocolate until fully melted and smooth. Into a second bowl, stir in the vanilla extract. Leave the third bowl plain.
Press plastic wrap directly onto the surface of each bowl and chill until very cold (about 40°F), at least 4 hours.
Stir the strawberry puree into the plain chilled custard until evenly combined.
Churn the chocolate base in the ice cream maker until soft-serve consistency, 15–20 minutes. Spread it neatly along one long third of the chilled loaf pan; return the pan to the freezer while you churn the next flavor.
Churn the vanilla base until softly frozen, 15–20 minutes. Spread it into the center third of the pan; return the pan to the freezer.
Churn the strawberry base until softly frozen, 15–20 minutes. Spread it into the remaining third. Cover the surface with plastic wrap and freeze until firm enough to slice, 4–6 hours.
To serve, lift the ice cream from the pan, peel off the wrap, and slice crosswise to reveal the three stripes. Let slices stand 2–3 minutes to soften slightly before serving.