Drawing terrain

It depends on what you want to do. Quad trees are a popular way of subdividing terrains, but you could also use an octree or a number of other structures to divide the world.

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Would an oct-tree help/make it easier with LOD stuff?

Well.. since a terrain is essentially a 2D function, and the chances are that polygons are added, in some fixed pattern (At least in simple engines with no LOD implemented)... then a quad tree is the choice. If you implement some very complex LOD method, then perhaps an octree could prove more useful. In fact... if the polygon placement is completely uniform and naive (with no LOD) then you may as well make your world tiled (this is what a quadtree would generate in a uniform poly distributed world). The other advantage of a tiled system, is that each tile can be treated as a normal game object... and thus could simply be handled by whatever LOD method you use for the rest of your engine. Basically it boils down to this, the method you choose is strongly dependant on the size, detail and potential use/flexibility you need from your terrain, thus there can be no definative answer.