I haven't played ffx in a long time so I don't know the exact name of the sphere but...
*******************POSSIBLE SPOILER ALERT************
Ok now that's over... near the end of the game you can get some type of sphere that I believe there are only a few of in the game (but maybe you can get some from creatures, I'm too lazy to look in my book). Anyways these spheres teach one character a move already known by another character. So (in my instance I did it with firaga) take yuna, then give her a high-end black magic spell. You will quickly find that yuna has a much higher magic attack score then lulu does. So then yuna will cast magic stronger then lulus and still be able to heal. Of course there will be certain problems with this and my guess is that alot of you already knew this, still you should try it if you haven't.