Roles can be the same or completely different. It's based on the Pokemon's movepool, abilities and stats, just like how the regular metagame categorises Pokemon. Pokemon that evolve into highly useable evolutions might themselves be unusable in LC, e.g. Happiny & Chansey/ Blissey, and the opposite is also true, e.g. Meowth & Persian.
Gible is used as a Sand Sweeper in LC, since Sand Veil is not banned in this tier. That might change in Gen VI, which would mean that Gible would lose its niche unless it get access to Dragon Dance.
Aron is commonly used offensively in LC. It usually carries either band or Rock Polish, along with Rock Head ability. It's not good defensively because of the prevalence of Water types in LC.
Larvitar doesn't have Sand Stream, it has Guts, and is commonly used with a status orb + Dragon Dance as a physical sweeper. Hippopotas is the only sand setter in LC, and it works like Hippowdon does; it's a physically defensive tank.
Happiny is not what Chansey and Blissey are. It has no access to Wish or Soft Boiled, has very poor offensive and defence stats and has a small movepool of support moves. The only reason to run it is for moves like Aromatherapy/ Heal Bell and T-Wave.
Mantyke is a common threat in LC, while Mantine is NU fodder for any electric type. Mantyke can hold Eviolite, therefore boosting its 120 sp. def even further, allowing it to run a Rest/Talk set, or it can run a Rain Dance set and be a Swift Swim sweeper.
Drifloon is unbelievable in LC because of Unburden Acrobatics. Not only does it deal significant damage, it'll then be fast enough to outspeed the entire tier to set up Destiny Bond.
Pokemon in LC have no ranks. There are some Pokemon that are too much of a threat and therefore banned from LC:
However, LC does have Speed tiers. While speed is important in all tiers, it's more important in LC because everything's frail, especially if they run berry/ Life Orb over Eviolite. Therefore base speed is important, especially when you're up against Aipom and Meowth since they will always run Technician Fake Out.
If you want to read up on LC:
BW LC Guide
LC Speed Tiers