In a medium saucepan, combine heavy cream, sugar, lemon zest and salt over medium-high heat. Bring to a simmer, stirring frequently to dissolve sugar. Simmer vigorously over medium or medium-low heat until mixture thickens slightly, about 4 to 5 minutes. (Watch carefully as you don’t want the mixture to spill over the saucepan. Stir if needed to prevent the mixture from spilling over.)

Remove from heat and stir in the lemon juice. Let the mixture sit until it has cooled slightly and a skin forms on top, about 20 minutes.

Stir the mixture, then strain through a fine-mesh strainer into a measuring cup with a spout (you should have about 2 cups). Discard the lemon zest.

Pour the mixture evenly into four 8-ounce ramekins or small bowls.

Refrigerate, uncovered, until set, at least 3 hours. Cover with plastic wrap once cooled and set. Custard can be prepared one day in advance.

Allow berries to sit at room temperature for an hour before serving. To serve, top each lemon custard with berries (about 1/3 cup per custard).