Remove the zest of 1 lemon in wide strips with a vegetable peeler. Juice both lemons to make about 5 tablespoons. Chop 1 cup of the strawberries and combine with 1 tablespoon granulated sugar and 1 tablespoon lemon juice in a bowl; set aside to macerate while you make the pudding.
Meanwhile, whisk the remaining 1/2 cup granulated sugar, the cornstarch and salt in a medium bowl. Whisk in the egg yolks and 1/4 cup half-and-half until smooth. Bring the remaining 1 1/2 cups half-and-half and the lemon zest to a boil in a medium saucepan over medium-high heat. Remove from the heat and let sit 10 minutes to infuse. Gradually whisk in the sugar-yolk mixture, then the remaining 1/4 cup lemon juice.
Return the saucepan to medium-high heat and cook, whisking constantly, until the pudding comes to a boil and thickens, about 3 minutes. Continue cooking, whisking constantly, about 1 more minute. Remove from the heat and whisk in the butter until smooth. Strain the mixture through a fine-mesh sieve, pressing it through with a rubber spatula; discard the lemon zest.
Divide the macerated strawberries among 8 clear plastic cups or glasses; top with the lemon pudding. Press plastic wrap directly onto the surface of each and refrigerate until set, at least 4 hours or overnight.
When the pudding is set, pulse the remaining 3/4 cup strawberries in a mini food processor until smooth. Beat the heavy cream and confectioners' sugar in a large bowl with a mixer on medium speed until soft peaks form, about 1 minute. Add the strawberry puree and continue beating until stiff peaks form. Top the pudding with the strawberry whipped cream and sprinkle with the crumbled cookies. Top with sliced strawberries.