Does it make sense to let a colleague know about his repeated misspelling?

Let it go, while the typo is limited to emails. Emails are frequently written hastily and certain typos can be common or made on purpose to type less, or even for fun (I do sometimes this in my language, to mimic certain dialectal expressions).

If, instead, the typo appears in, for instance, a paper or other public document you're jointly writing, then correct it as you would correct any other typo in the paper.

At some point you're going to edit a joint paper and correct "alot" into "a lot". It will be a very emotional moment for both of you. "I've been spelling it wrong this whole time and you didn't tell me!!" Tell them now. Tell them the truth, which is that it's starting to become a distraction for you (proof: you wrote this Q).

This isn't your great Aunt writing "the dogs were all their" on your yearly birthday card. You're eventually going to have to tell this person about mistakes in proofs, and argue with them over ideas. There should be some comfort level, esp. after years of working together.

The one thing to watch for is the special rule that any grad student can have any lesser-rank kicked-out of any program, anywhere in the world, for not showing proper respect. To be serious, in my mind you're both grad students. I had to look up "pre-doc" and read it twice and I'm still not sure how this other person outranks you (you haven't been accepted into a PhD program?)

I am not a native speaker and I was very happy when a colleague told me about a repeating spelling mistake of mine. If you want to do it discretly,just write him a quote were he mispelled it and say something with a lot about this quote.

Dear Mister X,
your wrote

"Alot of assumptions went into this study"

A lot of work has to been done, to make this work. We need another day in the lab

Or simply tell her.

Dear Mrs. Y, I agree with the proposed changes in your last email. I also think I noticed a bug in your spell checker, it always says "alot" instead of "a lot".

Kind regards Phd Student S.