Reserve about one third of your strawberries and place them in the refrigerator. These will be for topping the icebox cake after it chills. Toss the remaining strawberries with the strawberry jam and set them aside for assembling the icebox cake.
Using a stand mixer fitted with the whisk attachment, beat mascarpone cheese, vanilla extract, and lemon zest. With the mixer running on medium speed, slowly pour in the cream followed by the powdered sugar. Gradually increase the speed to high and beat until stiff peaks form. Scrape the sides and bottom of the bowl occasionally.
Assembly: Spread a thin layer of whipped cream on the bottom of an 8x8 square baking dish. Place one layer of graham crackers on top of the whipped cream. Break the graham crackers as needed to cover the bottom as much as possible. Top with one-third of the whipped cream, spreading it into an even layer. Top with half of the jammy strawberries. Repeat: graham crackers, whipped cream, strawberries, graham crackers, whipped cream. Hold off on adding the strawberries on top until after chill time (remember: these are the strawberries you have reserved). Cover with plastic wrap and refrigerate at least 6 hours, up to overnight (see note).
Add the reserved strawberries on top. if desired you can toss them with a little bit of jam to make them glossy and extra sweet. Serve chilled.
Notes
Chill time: The longer this chills the softer the graham crackers will become. I like the texture best after about 6-10 hours of chilling. If it chills overnight the graham crackers will be much softer.