Place cookies in a food processor; process until finely ground. Combine cookies and 3 tablespoons sugar in a bowl. Add 6 tablespoons butter, and mix well until crumb mixture holds together. If needed, add remaining 2 tablespoons butter. Transfer cookie mixture to a 6-inch springform pan, and pat out evenly to make the crust, lining sides of pan only about 3/4 of the way up. Place in freezer while proceeding.
Combine cream cheese, lemon juice, and remaining 1/3 cup sugar in a mixer, and beat until combined. Lightly whip cream to soft peaks, and fold into cream-cheese filling. Remove crust from freezer, and pour filling evenly into pan. Cover with plastic wrap, place in freezer for 30 minutes, then transfer to refrigerator until firm, at least 30 minutes, or up to 24 hours.
To serve, pass half the raspberries through a fine strainer to puree. Serve slices of the cake with whole raspberries and puree.