I've already posted my deck build in LoD topic
Zombies is one of the most awful matchups for LoD because its early and cheap removal (which my low end is based on) kinda doesn't work vs them. I run only 2 non-black removals but that's not the case - the most annoying thing is Undying that ruins all your removals and sweepers.
I mean, with LoD I don't have any problems with other aggro-decks but DW... Even sweepers don't work against it - 2/3 of their zombies will likely return from the GY instantly (undying, Cruel Revival) or a turn-few tuns after (Gravecrawler, Reanimate, Lord of the Undead). And their bombs include a guy that gives undying to everyone and a 6/6 that multiplies his zombie army every turn... Awful, awful and OP deck.
I think you are underestimating the meta.
That being said, here is what makes a deck top tier in this meta:
1. Strong turn 1 and two plays, and lots of them. For a classic example, just look at humans, zombies, and elves.
2. Tons of removal. Again, look at the top 3 here. All 3 of the old top 3, plus izzet, have tons and tons of removal. This is why they are the top 4.
3. Constistency. Avacyn and elves are good examples. Or frankly samurai, although it isn't a top deck. Samurai doesn't have the removal to be a top deck.