Was this movie aired before the last episode of Lizzie McGuire?

No, the episode of Lizzie was aired and then the movie came out.

The last ep of Lizzie involved Gordo realising he had feelings for Lizzie before they headed off to Italy.

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Yes. The movie is intended to be a grand finale to the television series, but season 2 aired out of the intended order, and the final episode didn't air until 2004, nearly a year after the movie came out.

Disney released all the episodes out of whack. The yearbook episode is technically the last of the television series, and the movie is the finale.

-Who is it?
-It's Grandpa. And it sounds like he's gotten into the horseradish again.

The way I heard it: This movie was supposed to lead into her high school years and have a sequel. The success of the movie led to Hillary Duff asking for more money but her Disney contract locked her salary in. When she refused, that led to the cancellation of the series.