First up, meshes and textures are two different things. The former, what this is about, is the 3d model, the latter is the the paint on them. The resolution of the texture usually has no impact on performance as long as you don't run out of VRAM.

On to the actual question: To a certain degree, yes, there's usually a settings that changes how aggressive the LOD system is at reducing and what's the max level of detail is. However, even on ultra most* modern games will still employ some sort of LOD, because rendering everything at max is just so ridiculously for almost no benefit, that it's just wasteful.

*: Some games can get away without a LOD system, for example a top-down game with a fixed camera distance. There you can directly optimize the meshes based on how far they appear from the camera.