Grandma Vicky is the grandmother of Vicky, whom was likely named for her. She is one of the oldest known member of Vicky's family, save for the other time frame related Vicky clones such as Vicky the Kid.
She bears an incredible resemblance to Vicky, and it is possible that Vicky is named after her. She wears glasses, and her hair is pulled back in a bun. She also wears green like Vicky does, only with a white shirt underneath with a frilly neck. Her pupils are colored pink.
Not much is known about Grandma Vicky, other than that she created (or, if she is anything like her descendant, stole and took credit for) "Grandma Vicky's Old Country Style Lemonade", a delicious tasting lemonade. Vicky uses slave labor to manufacture her lemonade by keeping the children she is babysitting locked up in a dungeon underneath her lemonade stand, the children are forced into squeezing the lemons. Any other information is purely speculative, including whether or not Vicky's mother or father is her child.
It is also very possible that Grandma Vicky was made up by Vicky to sell lemonade.