Make the mousse: Puree halved strawberries in a food processor. Pass through a very fine sieve into a bowl (you should have about 1 cup puree). Stir in 1 tablespoon lemon juice; set aside.
Melt chocolate in a medium heatproof bowl set over a pan of simmering water, stirring until smooth; set aside.
Put 1/4 cup cool water into a small bowl. Sprinkle gelatin over top; let stand until softened, about 5 minutes. Stir 1/4 cup cream and the confectioners' sugar in a small saucepan; bring to a simmer over medium heat. Add gelatin mixture, and stir until gelatin has dissolved. Pour into bowl with the melted chocolate, and stir until smooth. Whisk in 3/4 cup strawberry puree; reserve remaining 1/4 cup puree.
Put remaining 1 3/4 cups cream into the bowl of an electric mixer fitted with the whisk attachment. Beat on medium-high speed until medium peaks form. Whisk one-third of the whipped cream into the chocolate mixture. Fold in the remaining whipped cream using a large rubber spatula. Refrigerate 1 hour. Stir 1 tablespoon lemon juice into the sliced berries. Fold berries into mousse; refrigerate 1 hour.
Preheat oven to 425 degrees. Make the cake: Coat a 12-by-18-by-1-inch rimmed baking sheet with cooking spray. Line bottom with parchment paper, and spray parchment. Dust with flour, and tap out excess.
Put eggs, egg yolks, and sugar into the heatproof bowl of an electric mixer set over a pan of simmering water. Whisk constantly until the mixture is warm and the sugar has melted, about 2 minutes. Attach bowl to mixer fitted with whisk attachment. Beat on high speed until egg mixture is pale, thickened, and has cooled, about 6 minutes.
Remove bowl from mixer; sift together flour and salt over the top of egg mixture, and sprinkle with lemon zest. Using a large rubber spatula, carefully fold the flour mixture into the egg mixture, cutting through center and lifting gently over sides. When the flour is almost incorporated, pour butter down side of bowl, and gently fold in to incorporate.
Pour batter into prepared baking sheet; smooth top. Bake until center springs back when lightly touched, 7 to 12 minutes. Invert, and unmold cake onto a parchment-lined wire rack; peel parchment from cake, and let cool completely.
Assemble the cake: Cut cake crosswise into 3 rectangles. Set one layer, top side down, on a wire rack set over a rimmed baking sheet. Brush with half of the remaining strawberry puree. Spread a 3/4-inch-thick layer of mousse over the top (about 2 cups mousse). Top with second cake layer, top side up. Brush with remaining strawberry puree, and spread with a 3/4-inch-thick layer of mousse. Place third cake layer on top, top side up. Refrigerate at least 2 hours (preferably overnight). Trim sides of cake to be straight.
Make the ganache: Bring cream just to a boil in a small saucepan over medium-high heat. Pour hot cream over the chocolate in a medium bowl; let stand 5 minutes. Stir until smooth. Stir in salt and lemon juice. Let stand until ganache is pourable and has cooled slightly. Pour ganache over top of cake, allowing it to drip down sides. Refrigerate assembled cake 1 hour before serving. Using 2 large spatulas, transfer cake to a serving platter. Garnish with strawberries.