Usually engines clean the color and depth buffers every frame. And, of course, also render everything every frame.
Some engines allow you to tell them to not clean the buffers, but they would still render everything every frame. Which can yield some trippy results, including trails of images in the void (where there was nothing to render on top to replace them).
Having some things render less frequently than others is usually not a feature.
If we are not talking about disabling clearing the buffers, then the behavior I would expect is not double images, but having the object appear one frame, disappear because the engine cleared the buffers and rendered everything else, and then some frames later appear again for a single frame and so on.
You might hack it by rendering to a texture/viewport and overlaying the result※, except, of course, render that less frequently. But it would stay in place in the screen as the camera moves.
I don't know the details of your terrain system, but even if it does not move, the camera does. And assuming the camera has moved but the image of the terrain has not been updated, it would look wrong.
You could try further hackery to move the overlay on the screen according to camera motion. But it won't be perfect, as you are working with a 2D image at this point, so the perspective won't change. And also moving the overlay can't reveal parts of the terrain that were outside of what you rendered.
※This is similar to what some games do for first person weapons so they don't clip into the scenario geometry. It is also similar to some old school crowd solutions that render a cluster of objects once and repeat it on the screen.
About level of detail, most of the time the model used the last frame is the same you want to use this frame, since you only swap models when the object passes some distance threshold. If you swap the model a few frames late it is unlikely to be a problem, and if it is, we are talking about popping.
Be aware that often this swap is done in CPU, not GPU. So this process does not need to be tied to the render frequency... While doing it faster than the render frequency is wasting effort, you can do it less frequently with moderate impact... Unless the player is moving way too fast for the frequency you pick.
Updating the level of detail more or less frequently based on the speed at which the camera moves might be a good optimization.
I remind you that rendering is not the same as updating. You might have object skip update/process/tick/whatever-your-engine-calls-them calls or update in a separate thread with a different frequency, and still have them render normally.