Lexicon is WordGirl's home planet. When she was only an infant, she left Lexicon on a spaceship piloted by Captain Huggyface. After hitting an asteroid, Huggy saved them both by crash-landing on Earth.
The baby Lexiconian was found and adopted by married couple Tim Botsford and Sally Botsford, who named her Becky. They kept Huggy as a pet and named him Bob. Three years later they had a biological son whom they named TJ who became Becky's adopted brother.
In the episode "WordGirl Makes a Mistake", during a flashback while Becky was explaining how she came to Earth, we see a dome-like city in the background of Lexicon, possibly indicating that there is other life on the planet.
Not much else is currently known about the planet Lexicon. It seems that natives of the planet exhibit super powers on earth. This is a concept rather obviously based on the "Superman" mythos with Kal-el and Krypton.
The word Lexicon means a word book or dictionary, which is an appropriate place of origin for someone who has been called "the living dictionary." The word's second definition - the vocabulary of a particular language, field, et cetera - is also quite fitting.