I've always thought luck had something to do with critical hits. For FF8, it might have something to do with limit breaks and how often you get them (ever notice how occasionally, you get the option to use a limit break even if you're not on critical health?) Maybe it also has something to do with GFs and their Boost ability (e.g. sometimes, not matter how hard you try, you can only get Quezacotl up to 130 because the little red cross stays up longer. Usually, it'll be around 150-160. And occasionally, you get less of the little red cross and can get up to 170-180.)

But that's just my two cents.