I don't volunteer information about why I left, though some application forms may ask for it, in which case, you do need to put something. I can provide the reasons if asked, but over time, people do move on and change. And no one is likely to be totally honest if the real reason is something like, "the manager turned out to be a narcissistic, sexist, incompetent wanker, and I was finding it increasingly difficult to get out of bed each morning and go and face all the back-biting in the team." The company you leave may not know why some people go, just that they gave notice, then left.
I'd probably just say that the second job ending gave me an opportunity to think about what I wanted and the new job didn't live up to its promise and wouldn't enable me to fulfill my goals."
She can't lie on a reference, but she can state the bare facts, "orangetree was employed here between September and December 2016" or whatever.
I wouldn't worry too much -people get let go because of reasons like funding cuts, too, and you've few rights when you've only been there less than 2 years, so they're most likely to go - people do go on to get other jobs.