OK. The first thing I did is open the SketchUp model and purge unused content. There’s a lot of excess stuff.
There are some overly large textures, too. Those will slow down rendering in LayOut.
Even after purging the SketchUp model, there are a huge number of edges and faces in the model.
A lot of those edges come from elements like the key and all those molding profiles.
Although the edges aren’t displayed in the viewports, LO has to consider them for rendering as vector line work. Removing those things from the model would help but if you are dead set on keeping them, tag them and turn off the tags for the scenes where they aren’t visible. There really should be no reason to have all those molding profiles in the model anyway. If you want them to use in projects, the profiles should be saved into a component collection so you can drag out whichever one you need for the project you are working on.
You could simplify the model by removing the duplicate stuff like the walls, roof, skylights, etc. at the bottom of this screenshot. You should be able to create every view you need from the main model. Eliminating those duplicates would reduce the number of edges that LO needs to think about when rendering.
Although it won’t affect rendering times in LO you should be ensuring correct tag usage in your models. Here’ I’ve fixed it.
FWIW, Purging the unused stuff in the model and reducing the size of the remaining large textures reduced the SketchUp file size by 43%.
I also noticed in the LayOut file that you have multiple .skp references for what was ostensibly the same SketchUp files. It looks like during the time you have been working on the project you’ve inserted different revisions of the .skp into the LayOut project instead of sticking with just one.
Two of them aren’t actually used but they are bloating the LO file.
Purging the unused files from the references and the slight cleanup I did on the .skp file slimmed the LO file down by 74%.
If you take care of getting rid of the excess stuff in the model you can improve things quite a bit in LO.