If I have the desktop version of Lightroom and want to also have web access remotely is there a way to still use my desktop version and also access remotely if I want to do edit either way. I want to be able to store my photos as a "hard copy" on my harddrive at home
You can install Lightroom on home computer and you can do the import, edits & export from Lightroom, now let say you want to access the home system remotely from the different location, yes you can open the Lightroom and do the edits on the existing images in Lightroom.
You won't be able to import images in Lightroom using the remote system.
There are many ways to get files of any type from a mobile device or notebook computer to a home computer from some other location over the internet.
All of the Cloud services, FTP server set up on your home desktop, MS Remote Desktop and others.
Nothing IN Lightroom. Yes there is LR Mobile but that isn't exactly what you are looking for, IMHO.