In a large bowl, beat the softened cream cheese with a hand mixer on medium speed until completely smooth and fluffy, about 2 minutes. Scrape down the sides and beat again until no lumps remain.
Add the sweetened condensed milk, instant pudding mix, cold milk, and vanilla extract to the cream cheese. Beat on medium speed until thick, smooth, and slightly aerated, about 2–3 minutes.
Fold in half the container of whipped topping using a rubber spatula, using gentle sweeping motions to keep the mixture light. Refrigerate the pudding base for 30 minutes to firm up.
Toss the banana slices in the lemon juice to coat lightly.
In a 9×13-inch baking dish, arrange a single layer of Nilla wafers on the bottom, overlapping slightly. Layer half the banana slices over the wafers, then spread half the pudding mixture evenly over the bananas.
Repeat: another layer of Nilla wafers, remaining banana slices, remaining pudding.
Spread the remaining whipped topping over the top. Crush a small handful of Nilla wafers and scatter over the whipped topping.
Cover tightly with plastic wrap and refrigerate for at least 4 hours (overnight is best). Add fresh banana slices to the top just before serving if desired.