First of all, GoogleDocs has some issues with larger documents. Practial experience showed a limit of 50k words on an Android Samsung Tab 6 Lite tablet, as well as 100k on a Ryzen 1600 PC.
Split your documents in multiple parts if you run into this effect.
Lagging when typing and searching
Did you install Grammarly? If you did...
Fix, part 1
In spite of being in Beta for ages, Grammarly still misbehaves sometimes in combination with GoogleDocs. I found it to crash my browser now and again, so I disabled Grammarly for use on all but specific sites.
To do that:
1. Right click the Grammarly icon
2. Manage Extensions
3. Site access: on specific sites
4. Add the sites you want to use with Grammarly
Not there yet...
Now Grammarly should no longer affect GoogleDocs, but it does!
Go into GoogleDocs, and you'll see an 'Off' imprinted over the Grammarly icon.
Now load a large document, and try Control+F, and do a couple of searches for specific phrases. If GoogleDocs suddenly responds slowly you're suffering from a similar problem as I did.
(I don't know if this is Grammarly, or GoogleDocs, or the Chrome browser, or my specific machine that causes this problem.)
Fix, part 2
5. Left click on the Grammarly icon
6. Click 'Reload'
The 'Off' on top of the icon is still shown. But if you click again on the Grammarly icon, it now shows the Grammarly menu. Is it on? Or off? Who knows.
7. Now disable all toggles
From this moment on, your GoogleDocs is lightning fast again. Try Control+F a couple of times to verify that is the case.