Hmm, well, hearing them side by side... I can kinda hear a similarity. The one in Lizzie McGuire goes faster than the initial notes of the Chrono Cross one, but I think they do sound alike. Though I can't really say for sure.
Also, I don't think it would make things moot if the Chronopolis track sampled anything. Actually, Chrono Cross existed before the show, so if something happened, it would be the show sampling the CC track. If there was such thing involved.