If Limbo is a platformer then so is Lemmings.

Ridiculous statement, those games are nothing alike.

They have far more in common than Mario/Limbo or Sonic/Limbo.

Die until you work out how to solve the puzzle, very little platforming skill required, it's Lemmings but you only have one lemming.

Lemingbo.

I agree that Limbo has little to do with Mario, but 3D Mario also has very little to do with 2D Mario. The platforming genre is more diverse than Super Mario Bros. Limbo's gameplay involves a great deal of environmental challenges, and that's exactly how I would characterize a platformer. Admittely it's more a puzzle-platformer than a pure platformer.

So Lemmings is a platformer then?

This retreat is almost as ridiculous as it is tiresome, but it's made more egregious by the problem that it's not really related to the discussion you were having.

There's a reason for why the Wii has a more diverse library of very popular games. Nintendo is the most diverse publisher in terms of genres by quite a large bit.

If you look at Nintendo's games 1.5 million plus sellers (I picked 1.5 million rather than 1 million because it removes the issue of what to do with remakes)

5 2D platformers
4 sports games
3 mini games 
2 fitness games
2 3D platformers
2 action adventure games
1 third-person shooter
1 first person shooter
1 RPG (2 if you choose to count Super Paper Mario, in which case, move one from 2D platformers to here)
1 Simulation game
1 fighter
1 racer 
1 music game

(I may be missing a game or two)

There's essentially a game in every genre. The only two I'd say are lacking from the list is "sandbox" and "strategy". For strategy, the problem isn't the lack of the games, it's that they're not selling. You have both Fire Emblem and Battallion Wars, and if things had gone as they intended, you'd have had a Pikmin game too.

The only genre Nintendo really makes an abundance of games in is 2D platformers.  Apart from that, they've made at least one well-selling game in every single genre, with the exception of sandbox.

Sources?

I would say no. It's a puzzle game pur sang. A platformer in my book is a game in which you control one character directly where you run, jump and perform various other moves to overcome environmental obstacles and challenges, like jumping over ravines, dodging objects, pushing buttons and pulling levers, etc. until you reach the end of the area/level/world/whatever. The most important skills to be able to play a platformer is agility and good hand-eye coordination. Braid is only part platformer because the emphesis is on problem solving and not on on-the-fly reaction. Lemmings obviously doesn't have any pure platforming elements at all. Limbo, however is a balanced mix of basic run, jump and dodge gameplay mixed with minor problem solving.

Could you quote the OP and highlight where that claim is made?