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One of my main character's traits is that she has some superstitious beliefs. That trait is not essential to the MC, but everyone in the era of my story is. I'm contemplating a plot point near the end that the reader might perceive as deus ex machina, but the plot point isn't the actual climax, it's a faux climax.

To bring the idea home, my MC is one who believes good people are afflicted with calamities, only to be corrected and restored by a superpower without much effort on one's behalf. Then an event happens (like some relative wins the lottery and promises to help) that the MC thinks is the solution to all problems, only to discover this solution is not happening, or it made things even worse.

If the reader knows that the MC is superstitious would that be enough foreshadowing for the faux climax I'm considering? Or, would they think its a cheap shot on my part? I'm thinking of this because it could be the last lesson my MC needs to finish her arch.

Actually, the faux deus ex sounds pretty good.

That makes it all about the characters perception of the events. Just be sure that you have enough clues leading up to the event that after the reader finds out that it is not real, the readers can say, "of course, I should have seen that."

A deus ex machina actually does solve the problem.

I can't tell, from what you have written in your question, if winning the lottery eventually does solve all her problems. If it does not immediately but does eventually there is no escaping that fact that you used a deus ex machina, and this is not a good story. Her problems were not solved by her own efforts, or her own sacrifice, or her own imaginative solution, so she doesn't deserve the solution. No matter what "character growth" you have given her.

If the lottery win is not real, but the idea of it spurs her to solve her problems, then that is okay. If the lottery win is real but the only way to solve her problems is to donate all the money to charity or use it all to help somebody else, that is probably okay too. The miracle of the lottery win cannot solve her problem in any way.

But once it is "undone" (she will not benefit personally from any of the money), it can be used for her to learn a lesson, change her life goals, or accept a situation and then this personal change in her may provide the solution to her problem.

Like Dorothy in the Wizard of Oz, the way home was always with her, she was wearing the ruby slippers the whole time. But the WoZ is a kid-to-adult story; so Dorothy had to become a hero first, and save her friends, and be betrayed by the Wizard (he left without her) before she got her heart's desire.

You can't use a true deus ex machina "safely", you cannot solve the character's problem with any kind of million-to-one payoff. A satisfying ending must be a result of character, of bravery, of sacrifice, of risk-taking, of resolve, of selflessness, of one or more of the aspects of personality we find admirable, perhaps enough to bring us to tears.

Being lucky isn't one of those. In fact being lucky is one of the things many of us can resent! We use dismissive terms for it, like being born on third base, or being born with a silver spoon in her mouth, or being a trust-fund baby. It doesn't inspire admiration or sympathy; it generally inspires jealousy and resentment.

It seems to me that the sort of faux deus ex machina described in the question is perfectly acceptable. As to whether it works for readers, or is sufficiently foreshadowed, that requires reading the whole work, and is a question for the author's beta readers.

But then, I don't agree that a true deus ex machina is always bad for the story; it often is. But it can be part of a good story. An essential part, indeed.

For example, consider The African Queen by C. S. Forrester. (The book, not the movie based on it.) In this book, the central problem, to which the two MCs are dedicated for most of the narrative, is the destruction of the German gunboat Louisa, which gives the German forces total control of the river and lake. Their plan for this destruction fails totally, and the Germans are about to hang Charlie as a spy when Rose is rescued. Unwilling to hang a European woman, the German Captain of the Louisa sets them both on shore at a British outpost on the lake. From this same outpost, a few days later, an armed British speedboat sets forth after the Louisa. Having longer ranged guns, and twice the speed of the Louisa, it easily sinks her.

Neither the characters nor the reader had any idea that the British speedboat existed until after Charlie and Rose were set down at the British outpost. It is a pure deus ex machina. It solves the story problem with no effort by the MCs and would have done so in exactly the same way had they both fallen dead on page 10 of the book. Their efforts are totally irrelevant to the outcome.

The real story problem, unknown to the characters, is their character development, and the real climax is the scene in the gorge, where Charlie, at the insistence of Rose that they do not simply give up, repairs the damaged propeller, a task had considered far beyond his powers, and the two become lovers. Rose has learned to be less puritanical and convention-bound. Charlie has learned a sense of self-discipline and confidence. The remainder of the book develops these qualities further and displays them in action. The point is the value of the human spirit and the best efforts in the face of adversity, even if no result is achieved or no one ever knows of the efforts, much the same point as is made in the author's Brown on Resolution

In the movie version, the swamped African Queen destroys the Louisa using the improvised torpedoes that Charlie created at Rose's insistence, thus making their efforts successful, albeit only through an enormous stroke of luck. This removes the deus ex machina but reduces the emphasis on the character development, thus in my view weakening the story, not strengthening it.

Thus I say that in a rare case, a true deus ex machina can actually strengthen a story, by revealing that the apparent story problem wasn't the true issue at all.