In a small saucepan, combine the raspberries, sugar, lemon juice, and water. Bring to a simmer over medium heat and cook, stirring occasionally, until the berries have broken down and the mixture has thickened slightly, 8 to 10 minutes. Transfer to a bowl and cool completely.

In a large bowl, beat the mascarpone, heavy cream, sugar, and vanilla on medium-high speed until medium peaks form. Fold in the cooled white chocolate until fully incorporated and smooth.

Arrange a single layer of cookies in the bottom of an 8-by-12-inch/20-by-30-centimeter baking dish. Spread half the raspberry mixture over the cookies, then half the cream. Repeat with another layer of cookies, the remaining raspberry mixture, and the remaining cream. Top with a final layer of cookies.

Place the white chocolate and heavy cream for the topping in a heatproof bowl and melt until smooth. Pour over the cake and spread evenly. Spoon any remaining raspberry mixture decoratively over the surface.

Cover and refrigerate until firm, at least 4 hours and preferably overnight.

Serve chilled. The cake can be refrigerated, covered, for up to 4 days.