I'm not sure how this makes menstrual cycles " a lie". As far as I know, it's been known for years and years that it's occasionally possible to have more than one ovulation in a cycle (at least, I read that in a book which is a fair few years old).
Nor does it make using something like the fertility awareness method impossible, since that relies on observing the change in basal body temperature and cervical mucus around the time of ovulation (no matter when or how often ovulation occurs).
It is further proof that you can't use the "rhythm method" or any other variation of trying to find a "safe time" by counting days, but then more proof of that was hardly needed ....
So it's an interesting piece of research, but I think the article rather overstates how revolutionary it actually is.