I made a couple of plays that probably would have made them game less close. I could have gotten EM if I had not played my stilletto and/or saved my antimatter. Then again I may have also died sooner without them. I also intended for the fractal condors to draw out Rewind, but drawing out Scarabs works in a different way.
This isn't the best thing in the world to do. If you're not stupid/unlucky like me, you could possibly get a 50% win rate against Lionheart through deckout. Defeating him by sheer damage would also be possible, but only with a prefect draw and early set-up. Slowly, I started to realize that deckout has a higher win-rate when not mixed with any damage strategies.
The revised version of this guide will include what to do with each card for deckout, and more complex strategies that can be used in a good early situation for a riskier challenge. Either way, the games will be relatively long, and most of the time you're probably going to wish you were playing someone else.
Note: I only used VVV a couple times before originally decking out (and constructing a guide) for Lionheart. After a while, I realized the branching strategies had a few holes in them that were constantly leading to my failure. My experience with the deck now is still limited, but better than it was at the original writing of this guide.
Shards/Purify/Sanctuary - Play as soon as possible. Use other cards and Hasten before playing Shards.
Antimatter - Drop on a high ATK creature or Flying eternity, and undo after your defenses are set up.
> Riskier: Lure as many Vader-saders as possible and drop on these instead.
Condor/Fractal - Pull out very late, with a mostly empty hand, to prevent him from rewinding his own creatures.
> Riskier: Pull out slightly earlier, then drop Rain and allow them to attack over multiple turns.
Aflatoxin - Play early in the game on his creatures to clog his field, and/or very late in conjunction with condors.
> Riskier: Play
both early to clog his field, then Rain the cells late game.
Chimera/Sky Blitz - Almost totally useless. If you find a good way to use these to deckout, let me know : )
> Riskier: Sky Blitz can be used with buffed Condors for added damage.
Protect Artifact/Dagger - Play both in conjunction, or Dagger alone once no more Crusaders can be played or used.
> Riskier- Use Dagger to lure Vader-saders for Antimatter, and PA afterwards.
Heal - Use on your final turn before he decks out, or if you're in mortal danger. Math is important kids!
Jade/Permafrost - Play Jade only if Permafrost is not yet available. Permafrost is much better here.
Rain of Fire - Possibly use only if a few Scarabs have been quinted, to even the process slightly.
> Riskier: Destroy cells late-game after condors have been played.
Hourglass - Drop as soon as possible. Draw one extra card until you have a clear advantage, then draw more.
Early game:
You have to have Permafrost, Shards/Sancs, and Hourglasses out early. These are the major reasons I survived at all. Jade Shield can be played before Permafrost shield for minor defense, but otherwise should be discarded. PA can be used on any permanent, or discarded if need be.
If you draw both Aflatoxins early, you could use them on Saders or the first couple of Scarabs and attempt to fill his field. Slow incoming damage with healing and/or a shield (preferably the latter if not both). If you draw your Dagger before he gets Anubis or 
for the spell, you can play the Dagger, or save it until later.
Mid-game:
Assuming you survive the first few turns, you've likely got your defenses set up and plenty of hourglasses. If you played both Afla, his field will soon fill up, and you actually have a small chance of could executing The Combo, if you're really lucky. This seems like it would be an anomaly though.
If you played Dagger, wait for him to Endow it, and then Antimatter them (or Anubis) for the most possible healing. He also won't rewind anti-mattered creatures, so you want to antimatter one early to stay alive, re-antimatter it late so he quints it, and waste/discard the third.
Sky Blitz should be played as soon as you draw it or discarded, because it's useless if you try to deck him out. Play Purify as soon as you draw it, and Rain of Fire once he has three Scarabs. If you saved your dagger and don't wish to attempt a Vader trick, wait until you draw PA, and play them together.
Late game:
Stop drawing just before the time where he would deck out before you. Keep track of the amount of hourglasses he has every turn. By now you should only have Fractal, Condor, Heal, and possibly Chimera, Dagger, and Aflatoxin. If you still saved your Dagger, play it once his field is basically full and all his Crusaders have endowed themselves.
If you didn't use or discard your Aflas and Chimera, you can try a trick where you create Cells on your own field. If you do this, make sure it's on the same turn you fractal the condors. If you can get yourself a set of Condors (and possibly Cells), you can allow them to be rewound/eaten, so Lionheart is less able to prevent deckout.
Once he has 0 cards left, or 1 cards and 2 spots in hand, play the Heal, and end your turn. You'll automatically win because Lionheart can't draw his required cards. If you succeed in doing all this, and have a good amount of luck as well, you can lulz and watch Lionheart helplessly deck himself out.
