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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.