It is unknown if this is the same Penny Lamb that Jane is resurrected as. The only known recording of Legoland is of Penny and Ezra Lamb singing Eminem's song 'Stan', but the script is available for purchase in book form. Penny Lamb is a character in a play called Legoland, which is also written by Jacob Richmond and Brooke Maxwell.
The script for the musical does not answer this question either way – in fact, it leaves the decision up to productions by offering two different options for Jane Doe's video at the end of the musical: one showing her having a full life as Penny Lamb after being resurrected, or another showing her life as Penny Lamb before her death on the Cyclone.
Emily Rohm, who originated Jane in the Chicago Shakespeare production and multiple other productions through the years, believes that Jane was not Penny before the accident.
After The Ballad of Jane Doe, the other teenagers start to sympathize with her situation, throwing her a birthday party. Throughout the show, Jane accidentally scares the others, especially Constance. Jane is the last choir member to be introduced. She was buried as Jane Doe, and given a Catholic funeral. This made her unidentifiable, and since no relatives came to claim her body, her name is unknown. Jane died in the Cyclone accident, losing her head. Cassian student, and went to the fair with the choir students. Little is known about Jane's previous life.