As a partial answer, note that you will get extremely different results for P(H|E) depending on your choice of hypothesis H and evidence E. In particular, while naively E here is "Ms X won the lottery 4 times", I think you'd still be posting the same question if instead you'd heard that "Mr Y won the lottery 4 times", or more importantly, any other extremely unlikely positive-valence event ("Ms Z was struck by a bullet in the tiny area that happened to be protected by an object in her pocket", etc). Which means that your E should perhaps be "some lucky unlikely thing happened to someone at some point in history", which no longer seems very low probability after all.

Also the jump from "there's something weird here" to "the Christian god did it" is too big - even if we do decide that some extraordinary explanation is required, our hypothesis space should at the very least include other gods :) and perhaps more realistically, things like bugs in the lottery program, collusion with corrupt lottery officials, etc.

How many tickets did she buy?

I am asking because I have heard about people who after winning a lottery spent all the money on buying more tickets. If perhaps she used the same strategy, then the chance of winning the first lottery was maybe one in a million, but the later chances were substantially higher.

tl;dr - more data needed

I'm doing this as a comment, not an answer, because it's only slightly related to the specific question, but Matt Parker did some videos about similar "impossible" events and/or probability claims, and he includes discussions on why we tend to make errors like that, as humans.

How lucky is TOO lucky? — https://www.youtube.com/watch?v=8Ko3TdPy0TU

How did the 'impossible' Perfect Bridge Deal happen? — https://www.youtube.com/watch?v=s9-b-QJZdVA

Very odd, perhaps a year-old post (it did sound familiar, and I find I've already commented on it) getting reincarnated on the site is evidence of a higher power.