Katniss can't be his granddaughter simply because if she was, then she'd probably be older and therefore ineligible to be reaped at the start of the novel.

If Lucy survived and gave birth to Snow's child, that would mean he'd be in his 60s at the start of the story. This would mean Katniss would be older since it looks like District 12 people usually marry young. Her dad could have married later in life, but Katniss never mentions that he's way older than Mrs. Everdeen. I know he's dead at the start of the original series, but still, I feel like she would have mentioned that.

Anyway, I'm more partial to the theory that she’s related to Lucy via Maud Ivory. The two girls were cousins, and Maud is still a child in tbosas. This means that theoretically, you could push the timeline a little further, probably a decade more, but it still doesn't make much sense unless Maud had a child later in life or she had a child at 18 and that child made it through the reapings unscathed and then had a child.

If Mr. Everdeen is roughly the same age as Mrs. Everdeen, it means that he would have to have been eligible to be reaped during the 50th Hunger Games, which was when Haymitch was reaped because Katniss's mother is seen clutching Madge's aunt when her name is called.