Combine the softened cream cheese, confectioners' sugar, and salt in a medium bowl. Using a hand-held electric mixer, beat on low speed until the cream cheese is smooth and the sugar is incorporated. Add the heavy cream and beat on low speed until the mixture is smooth, stopping to scrape down the sides of the bowl as needed.
Increase the speed to medium high and beat until the cream is billowy and holds medium-firm peaks, 30 to 60 seconds. Add the lemon juice and zest and the chopped mint, if using. Stir briefly to blend.
Line up parfait glasses or stemmed wineglasses. Beginning and ending with the berries, evenly layer all the berries and all but about 2/3 cup of the cream into the glasses. Top with a dollop of the remaining cream and garnish with a mint sprig. The parfaits can be made an hour or two ahead of serving.