It may well be a RAM/VM problem. The larger the file the more ram & virtual memory it demands of LW & your computer. All OSX apps use VM. The best way to reduce this is to only show the windows open you're using at that time (eg: go to View>Hide library, monitor & connection windows.) Delete any old search results that are older than a few hours. Set your downlds to Autoclear. If you're not attending to LW at the time, then hide it in the Dock.

You can monitor how much ram & VM LW & other apps are using by opening the Activity Monitor found in your Utilities folder.

It might also be a good idea to limit computer & net use/activity when you reach the end of downlding those very large files.