Line a 9x13-inch baking dish with parchment paper or lightly grease it. Mix the graham-cracker crumbs, melted butter, and sugar until evenly moistened, then press the mixture firmly into the dish and chill for 15–20 minutes.

Beat the softened cream cheese until smooth and free of lumps. Add the sweetened condensed milk, lemon juice, and vanilla extract, then beat until the mixture is thoroughly blended.

Fold the thawed whipped topping into the cream-cheese mixture using a spatula. Use gentle strokes so the filling stays light and airy.

Fold in the very well-drained fruit cocktail and crushed pineapple. Make sure the fruit is not carrying excess syrup, since extra liquid can make the filling loose.

Spread the fruit filling over the chilled graham crust and smooth the top. Cover the pan and refrigerate for at least 4 hours, preferably overnight, until firm.

Slice the cake cold and garnish each piece with a little whipped topping, a cherry, or reserved fruit if desired. For especially firm pieces, freeze the covered cake for 30–45 minutes before cutting, but do not serve it fully frozen.