Gawd. Been doing genealogy research for 25 years, and have seen every crazy story under the sun, but this one is something else.
"Of all the gin joints in all the towns in all the world, she walks into mine"
Nothing is too improbable with genealogy.
You got me wound up now: his real name wasn't even Lewis Carroll. It was Charles Lutwidge Dodgson. This insane Jean Carroll person is just making a bad joke.
http://www.bbc.com/culture/story/20160527-alice-in-wonderlands-hidden-messages