I think you're not understanding LODs. LODs don't add any triangles to your model ... or they shouldn't.
Firstly, all models in game engines end up triangulated. So, even if you create a cube with six quad faces, you'll end up with a cube with 12 triangles once it's in the game engine. Game engines work with triangular faces.
Secondly, LODs are used to REDUCE the number of tri-faces a model has based on it's distance from the camera. So, if you have an NPC, for example, that is made up of 10,000+ triangular polygonal faces, that NPC doesn't need all 10,000 faces when further away since you won't be able to see all those details. Therefore, a series of LODs (LOD1, LOD2, etc.) can be created for various distances, each one having fewer and fewer triangular faces.
One of the reasons you may want LODs is because off in the distance, further from the camera, more objects can be seen, more objects can be fit on the screen. If an NPC is right in front of you, they will block a good bit of the background, so it's okay for them to have a large number of triangular faces. But if they are off in the distance, but still visible, they block little to nothing. As a result, you may see many similar NPCs. If they all kept 10,000+ faces each, then this could potentially be problematic on some PCs. So, with LODs, they might have 5000 each ... or 1000 ... or even less, depending on the distance. As an NPC were to approach you (or you the NPCs), you would hit different LOD stages as they got nearer the camera. This would not be ADDING triangular faces but, in effect, returning the model to it's original detail.
So, LODs are NOT about adding more triangular faces to a model, but about REMOVING triangular faces in order to decrease details that won't be seen in the distance in order to help your PC keep frame rates up, etc.
EDIT:
Many times you would create these LOD levels yourself, creating the additional models that would be used for LOD1, LOD2, etc. The engine would swap out the model based on the distance from the camera, using whatever LOD level is determined. However, there are engines that use AUTO-LOD. This automatically reduces a models triangular face count based on distance so you don't have to create these models yourself. You would still have the option of creating the LOD models yourself and using them instead, but just wanted to point out that some engines support this feature.
Intel i9-10900K 5.10GHz, 64 GB RAM, Nvidia GTX 1080 ti 11GB, Windows 10 64-bit, dual monitor display