Lily's ostensible motive is to keep the cookie (although she ends up giving it to Ken), so she uses the sleight of hand method to misdirect Dr. D. Perhaps her ultimate goal is to establish her control over the decision-making.

The real Monty Hall's motives are more complex. One might think that Real Monty wanted to save the show some money and trick the contestant into choosing the non-prize door. But if this strategy worked every time, either (1) the contestants would know to watch for the trick, in which case the contestants would win more than 50% of the time, or (2) the contestants would more often than not be fooled, which would lead (more often than not) to an "ooh" from the studio audience. Whether or not the home viewers caught on to this device, they would lose interest in the problem--there would have to be at least the perception of either (a) chance or (b) the skill / agency (or stupidity) of the contestant at work to encourage the viewers to watch. So while the ruse might have saved the show a bit of money, it would probably have lost them viewership, which would be far more costly than giving up a car or two. In other words, the contestant has to SEEM to have the chance to win and the chance to lose.

So it would behoove Real Monty to maintain the illusion of contestant skill (intuition) or the lack thereof. Contestants shouldn't be either right or wrong all the time.

If Real Let's Make a Deal contestants read the analysis of Marilyn vos Savant (or the Bayesian equation), they would change their initial choice, which means that over time, the contestants would tend to win the car. If the win bordered on likelihood, there would be less unpredictability / engagement from the point of view of the audience, and the Real Monty would probably revert to a subterfuge like Lily's, but not every time (and the purpose of the subterfuge would not be to save cash, but to increase audience engagement by increasing uncertainty).

Did Real Monty Hall resort to occasional subterfuge to shake things up? I watched the show often in my youth, and I have no idea.

But the ultimate determining factor from the show's point of view should be considered to increase ratings, not to save cash by manipulating the contestant to lose.