Heat oven to 350°F. Line a 9×13-inch pan with parchment, leaving overhang.
Combine graham crumbs, 1/4 cup sugar, and salt. Stir in melted butter until evenly moistened.
Press crust firmly into pan. Bake 10–12 minutes until set. Cool completely.
Cook strawberries, 1/3 cup sugar, and 1 1/2 tbsp lemon juice over medium heat until juicy, 4–5 minutes.
Whisk cornstarch with 2 tbsp water. Stir into berries and simmer until thick and glossy, 2–3 minutes. Cool fully.
Bloom gelatin by sprinkling it over 3 tbsp cold water. Let stand 5 minutes, then warm briefly until dissolved. Cool slightly.
Whip cold heavy cream to soft peaks. Set aside.
Beat cream cheese and powdered sugar until smooth. Mix in sour cream, vanilla, and 1 tbsp lemon juice.
With mixer running on low, stream in cooled gelatin. Fold in whipped cream gently until no streaks remain.
Spread filling over cooled crust. Chill 20 minutes to begin setting.
Spoon cooled strawberry topping over filling. Swirl lightly if desired. Chill 4 hours or overnight until firm.
Lift out with parchment. Slice into bars with a hot, dry knife, wiping between cuts. Serve chilled.