In the Dormouse's story, Lacie is an anagram of Alice.
The Dormouse tells Alice about three little sisters—Elsie, Lacie, and Tillie—who live at the bottom of a treacle well and live on treacle. Their names hide references to the real Liddell sisters, whose family circle was closely connected with Lewis Carroll and the origins of Alice's story.
Elsie represents Lorina Charlotte Liddell through her initials, L.C. Tillie refers to Edith Liddell, whose family nickname was Matilda. Lacie, meanwhile, is formed by rearranging the letters of Alice. The wordplay turns the apparently nonsensical tea-party anecdote into a small private joke about the children Carroll knew.
Readers sometimes confuse Lacie with Lorina because Lorina is the name behind Elsie, not Lacie. Matilda is connected with Tillie, while Edith is the person represented by that nickname. The Dormouse's story is also distinct from the Disney film's use of Twinkle, Twinkle, Little Bat.