The big question is whether the screen lock is on. If it is then you'll need to unlock it in order to access the files (which is reasonable: if not then the screen lock wouldn't protect your data very well). You may also need to change the connection mode from "charge only" to "MTP", depending on what your default settings are. These are all things that are easy if you can see what you are doing, and really quite tricky if you can't.
Though if you have a fingerprint scanner set up unlocking might not be a problem, so I'd give that a go before worrying about anything else. And you might be able to enter a PIN blind (assuming that it's just the display that's out and the touchscreen is working).
If you do need to see what you are doing, what sort of screen mirroring does the K20 support? The old MHL technology was great because with a suitable adapter you could connect it to a TV or monitor without having to do anything on the phone other than plug the adapter into the USB port, whereas if it relies on stuff like Chromecast you'll need to interact with the system to make that work in the first place. Some LG devices supported something called Slimport, but I don't know much about that. But if you do need to interact with it in order to get the file transfer connected being able to mirror the display one way or another may help.
