Yeah, Lion Heart will add something to your 255 STR and 255% ACC; the Lion Heart Limit Break. Basically, it's Squall's Omnislash. Its functionality is almost exactly the same, with the caveat that you have to hit the trigger at the appropriate times. Without Lion Heart, I wouldn't give you two cents for your chances against Omega.
Me, I didn't bother with the card game, so when I went to fight Omega, I was SOL on Holy Wars. So after a lot of trial-and-error I developed this method, which lets you beat him pretty easily without them: Get the No-Encounter ability on a GF that has it, and then blitz around the Islands Closest to Heaven and Hell finding the hidden draw points (press X). They all yield high-quality rare spells; Ultima, Meteor and the like. Triple is the only one you should really worry about; finding Ultimas and Meteors are easy enough. After you get every spell out of the draw points, kill shit for a while and come back later; the spells regenerate. There are four spells you're going to need for casting purposes in the battle: Haste, Aura, Protect, and Revive. The most important of these is Aura. I recommend Megalixirs in lieu of Full Cure spells, because they heal everyone and because you can refine 100 Megalixirs out of a particular card. Get as many of these spells as you possibly can; ideally, you should have 100 of each for each character, but that takes a damn lot of time, and I did it with less.
Your party for this fight is Squall, Zell, and Irvine with their best weapons (Lion Heart, Ehrgeiz, and Exeter respectively). Use the four Forbidden Magics (Ultima, Meteor, Flare and Holy) and powerful stat-building GFs like Bahamut to boost your STR and ACC to 255 and your HP to 9999; the HP is an absolute must. Also, jack up your Speed stats as much as possible; this is the key to this method, and it's where the Triples come in. The 60-70 range should be enough, but try for the 100s. Then, order your characters by their Speed stats; give your fastest guy Cerberus and your second fastest Doomtrain. Your third guy should have most of the spells you've set aside to cast. Make sure that if your characters have levels that are multiples of 5 that you've junctioned 100 Deaths to them; as soon as the fight starts, Omega casts L5 Death, and if you don't protect yourself you'll die right quick. Speaking of protection, at least one character should have Auto-Protect, and give someone Auto-Haste if at all possible; the GF abilities last throughout the fight. If one or more of your GFs have the Revive skill, so much the better. Finally, turn the combat speed down. Way down.
Now, to war: As soon as you can, cast Cerberus and Doomtrain in rapid succession; this will enable Triple on everyone and drop Omega's DEF to 0. Your third guy should triplecast Haste. Hit him a couple of times with normal attacks, and when your caster's turn comes around again, triplecast Aura. Now lay into him with Limit Breaks. Squall's Lion Heart looks like Omnislash and does slightly more damage; you can expect about 160,000 per use, provided you hit the trigger at the right times. For Irvine, use Quick Ammo; if you can hit the trigger fast enough, it does more damage over time than Pulse Ammo. You can expect each hit to do about 3000-4000 damage, and you can fire about thirty rounds of Quick Ammo with a decently fast trigger finger. For Zell, don't use his big combos. Instead, keep on alternating between your two basic hits for the entire time. If you're fast, you can probably manage about six combos per second, each of which will do about 5000 damage at 255 STR. If you're lucky enough to get the full twelve seconds, that's 30,000 x 12 = 360,000 damage. I didn't invent this technique myself; somebody on GameFAQS did. They termed it Armageddon Fist, and considering its potential to be the most damaging attack in the game, it's well-named. Take some time out from Limiting to cast Protect on everyone; if he uses Terra Break, Protect means the difference between life and death, even at full health. The idea here is to kill him before he uses it.
The key feature of this method is speed; Omega will hit you with plenty of bad stuff, much of which kills in one hit. But with the speed boost provided by junctioning Triples and putting everyone in Haste, you can get eight or nine moves for every move he gets, which means that as long as you don't forget to heal when you need to, you'll win. If you're really sitting pretty, draw some Forbidden Magic off of him to use against Ultimecia; it's the best opportunity to actually get a full stock of them.
