I hope you've had a chance to look at a map of Middle Earth. There is a lot going on - the landscape was formed by the need of Tolkien's narrative. Tolkien was a linguist, not a geologist. But he based his descriptions on the places he knew. So his landscape draws on the same geologic history that formed our own world.
Physiographically the Misty Mountains and the Ered Mithrin form long, linear topographic highs. These kinds of features are often indicative of tectonic stresses distributed over a large area. On earth, "active" tectonic boundaries tend to have these features. The stresses caused by one plate interacting with another deform the rocks along those boundaries. It's not unreasonable to think that the Misty Mountains indicate such a feature.
We can use the shape and orientation of the mountains to infer plate boundaries and the orientation of the stress. If you hold a phone book and push in with both hands, the book will bend. But the orientation of the bend is perpendicular to the direction you push with your hands - like so:
Deformation either from pushing on the phone book, or that caused by colliding tectonic plates, tends to be oriented away from the direction the stress is coming from. Since stress is coming from the left and the right, the least amount of stress is acting forward and backward (with regards to the above picture). So the deformation occurs in that direction.
Since the Misty Mountains are oriented North-South, we can reasonably assume the stress is coming from East-West. And since we have uplift (mountains), we probably are seeing the crust thickening at this boundary, such as happens when two plates converge on each other like India and Asia. If they were pulling away, we would see thinning of the crust - and perhaps a rift valley or three like we see in East Africa and the Arabian Peninsula.
So, we would probably make the same assumption for the Ered Mithrin. But would we be correct? It's not an unreasonable thought, since these are also a long linear uplift feature. But these are oriented perpendicular to the Misty Mountains, which we've already established as forming because the tectonic stress of two plates is oriented East-West. We need to adjust our thoughts if the Ered Mithrin is also forming due to converging plates. If, perhaps there were several plates - the plate below Mirkwood moving Northwest, into a plate on the other side of the Misty Mountains, and another North of the Ered Mithrin. This isn't easy to do all at once, so perhaps the collision forming Ered Mithrin happened first and the Misty Mountains formed later?
Perhaps - this could work, but maybe we should look earlier in time. It might be that an answer lies not with the most immediate pattern, but one formed earlier. Like the way you have a knotted ball of yarn and you can't undo the second-to-last knot until after you've undone some earlier, deeper knots.
For a complete overview of this series:
Part 1: http://pascals-puppy.blogspot.com/2013/12/unnatural-histories-lonely-mountain.html
Part 2: http://pascals-puppy.blogspot.com/2013/12/unnatural-histories-lonely-mountain_16.html
Part 3: http://pascals-puppy.blogspot.com/2013/12/unnatural-histories-lonely-mountain_9632.html
Part 4: http://pascals-puppy.blogspot.com/2013/12/unnatural-histories-lonely-mountain_1042.html
Part 5: http://pascals-puppy.blogspot.com/2013/12/unnatural-histories-lonely-mountain_5911.html