Is it possible to password protect access to a folder with your macOS password? I'm trying to figure out the best place for me to backup my Lastpass CSV and it seems like the best place to put it would be on my full-disk-encrypted macbook, but I would like to be able to require a password before someone is actually able to read it.

I know I can password protect a folder with a chosen password but that's likely something that will be forgotten.

Is there a way to set the permissions of a file to require the Admin password before viewing the contents?
You can always use Disk Image to mount an encrypted partition that you can write files to. You choose the password, so you could set it to be the same as the password for admin. It's pretty simple to do:

https://support.apple.com/en-us/HT201599