The issue you're facing is most likely an "internal storage" issue. A partition was most likely corrupted at some point during the flashing of something. That's why you can install onto the internal partition, but not from it; remember, TWRP is installed onto the "recovery" partition but if the main partition is already corrupted, all you're doing is going in circles wiping and flashing from something that is already corrupted . This issue hasn't happened to me on my Nook HD+, but it did happen on a rooted Nexus 6 with a Custom ROM, as well as a rooted Note 4 with a Custom ROM I had in the past. Only returning both phones to factory stock; to restore every partition to it's default state, and then installing the Custom ROM again fixed those issues for me. If you don't have the stock Nook HD zip to return the Nook HD to Barnes & Noble's stock OS, I'm sure I can find it somewhere on an old hard drive I have; I did have a Nook HD at some point in my life, but the Nook HD+ was a lot better for reading Manga so I got rid of my 7 inch Nook. If that still doesn't work, maybe you should try expanding the /system partition with REPIT; maybe the Nook HD doesn't work well without Gapps and they're necessary for the functionality of the LineageOS ROM on the HD version, who knows.I appreciate the offer, but unfortunately I have a Nook HD. I'm using the hummingbird version of that same Lineage build. It seems like it works fine without GAPPS thus far except for this storage issue.
I've tried wiping and reflashing the ROM and it still says I have 0 bytes free in the included files app. Trying to download anything with the included browser just crashes the browser, but I can install apks via an SD card, F droid, etc. just fine.
I can't see any folders when I plug the tablet into my PC either. I can open "Shared Internal Storage" just fine but nothing is there and I can't write to it.
If the ROM has been proven to work well for others, perhaps I made a error while installing? I followed OP'S guide (From a stock install) exactly, so I'm not sure what I could've messed up.