She looks similar to Plankton, except that she has glasses, dentures, lavender-colored puffy hair and wears an orange dress that has light green polka dots with pink lipstick. Unlike most other plankton in the series, she appears to have two eyes instead of just one, but in "Grandmum's the Word," she has one eye and however it was revealed that she is evil just like her grandson Plankton and wants to steal the secret formula for herself and rule the Krusty Krab.
She later appears at the end of the episode, where she angrily drags Plankton away from the formula and out of the Krusty Krab due to him stealing her belongings as part of a scheme.
"A Plankton Family Tree"
Lily, referred to as "Ella," appears on her family tree.
"Grandmum's the Word"
She comes to the Krusty Krab as it is her 90th birthday and Plankton promised that he'd own the Krusty Krab by then. Since he does not, Plankton fools his grandma by getting the Krusty Krew to cover for him. Throughout the episode, Lily checks out the Krusty Krab. When Lily asks for a photo with her with the formula, she takes off with a jetpack, fooling everyone. When she gets back to Shady Shoals, she gets a dream with her ruling the Krusty Krab. While she's sleeping, the Krusty Krew take the formula back from her.
A picture of her appears in Plankton's kitchen.
"The Ghost of Plankton"
She appears at her grandson's funeral, and is shocked when Plankton becomes alive (due to the Flying Dutchman possessing his corpse). Lily and the other attendees believe that Plankton faked his death as a joke, and start attacking him in anger.
In "Gramma's Secret Recipe," there was an error where Plankton stole her hair as part of a scheme, but she was still shown with hair after Plankton stole it. This error was later fixed in American re-runs and on the season 7 DVD release.
In "Gramma's Secret Recipe," she has two eyes, but as of "Grandmum's the Word," she has one eye like Plankton.
In "Grandmum's the Word," she develops a crush on Squidward, and she is even shown married to him when she dreams of world domination after stealing the secret formula.
In A Plankton Family Tree, she is called "Ella" instead of "Lily." It is unknown if this is another name of hers or if this comic is non-canon.
It is possible, if not likely, Ella and Lily are two separate characters and Lily is Plankton's maternal grandmother.
It is also possible that "Lily" is a nickname, as she says "Call me Lily," in "Grandmum's the Word."
She was completely unaware that Karen was her granddaughter-in-law.
She is 90 years old, while her grandson is already in his mid 70s, which indicates that she and one of Plankton's parents had kids at a very young age.