After hearing the reasons why the laning structure is the way it is on Summoner's Rift, I want to apply a little of this theory onto the TT.
My reasoning behind the two top one bot is simple I think. While bot lane has easier access to Red Buff, it is a shorter lane than top, with one entrance point for reliable ganks. I would put a solo lane champion with durability here, to maintain Red control, with the ability to take the small camps on either side of the map when they push.
Top Lane is the longer lane, but more importantly is closer to the top jungle. Two champions with strong sustained jungling capabilities should be able to secure the buffs, and maintain control over the important dragon, while tackling the less safe top lane. While the camps are down, he or she can continue to lane as usual.
Top Lane: Olaf, Nunu
Bot Lane: Yorick
This composition is designed to have Olaf do the maximum amount of damage, then resurrect him and have him do more. Top lane has SUPREME jungle control, and has a strong laner. Nunu has the built in smite, and can blood boil Olaf for extra damage. The nice part about this lane is both laners can jungle. Yorick is thrown bottom because of his solid lane presence (he can 2v1), and his ultimate on Olaf. He is also able to take the small camps in mid when he has enough mana. Red buff preferably goes on Olaf here.
Weakness? Lack of Hard CC. All three have a decent slow, but no stuns/knockups.
Top Lane: Malphite, Lee Sin
Bot Lane: Tristana
Turtling in threes happens, so a good way around this is to pack an AD carry in your composition, and have excellent tower seige abilities. I put two strong junglers top lane again, to secure dragon/buffs. Both Malphite and Lee Sin are also competent laners with durability, and some mobility. Great engage on Malph ult, and LS can hop around the map kicking and doing his tanky DPS thing that he does.
Weakness? The risk in this comp is running Tristana bottom. While (IMO) she is the safest AD with her jump and knockback, she may have a hard time versus two bruisers bottom.
I think a traditional AD support lane top would also work, but I think wasting the potential sitting in that top jungle sucks. I like the idea of soft jungling nunu quite a bit, and I like the idea of an AD carry. Vayne/Graves have been known to handle solo lanes, but I think being so far away from a turret in some cases could be extremely detrimental to their viablity, even if Blooboiled Vayne with the AS/MS sbuff on TT sounds great. I liked trist the most due to her safety.
I do not like running Shaco on this map at all. While his ganks can be devastating early, It allows me to run some riskier things like AD Sion, I only have to miss a creep wave to start farming at my turret.
Trynd is another jungler that could start soft jangling at level 4 or something.
What do you guys think?