Hi,
Lodi needs to be propagated form grafting to remain true to type. If you planted the seeds the apples would be a cross between Lodi and whatever variety pollinated it, and the results would be unpredictable.
Grafting is fairly easy to do and will return fruit in a few years. The best solution might be to plant new saplings to get more Lodi apples. I am really curious how Lodi came to be your favorite apple.
Mike