Does she qualify for the GC lottery if she applies? A very good question and she has every reason to be concerned. She came into the US, applied for and received benefits she's not qualified to receive as a visitor.
If she applies and get's selected, a visa will not be issued to her if she turns up in the system as having received benefits she wasn't entitled to receive. If this information does not show up at the time of the interview and she has a successful interview, she still has to live in perpetual fear of discovery in the US. She will face deportation if this information later turns up in the system even after becoming a LPR.
A woman from an African country came to the US a couple of years ago to have a baby. With the help of her hosts, she applied for and received medicaid. Four years after having the baby, she went back to the embassy to apply for a new visitor's visa since her current one had expired. Of course she was denied the visa as she showed up in the system as having fraudulently applied for and received benefits she wasn't entitled to. She's going up and down today asking everyone for guidance of where to send the payment for the care to as she's able to pay. But then, the issue isn't whether one is able to make the payment now or not, she's basically facing a life time ban from the US.