The method described by Cletus is one of the ways of getting the assets from one cloud account to another (though most methods will involve downloading and then re-uploading). Another could be exporting "as original" from Lightroom using the current account, then importing the exports to Lightroom using the new account. And then there is the Adobe Lightroom Downloader, which I wouldn't recommend as there are a few too many issues with that for my liking. As well as the inherent download/re-upload requirements, each have further issues.....the LrClassic method would lose any keywords and location data that may have been entered in Lightroom, the export method retains the keywords and location data but loses all album membership (though that could be circumvented by adding album-specific keywords to all images before the export.
Unless Adobe can come up with a way of seamlessly transferring the assets from the old account to the new account, without needing to download/upload, there's only one possible "solution" to effect the transfer without downloading. The basic steps are as follows:
1. Login to Lightroom (desktop or Web app) using your new personal account details.
2. Create a new empty album, which you then set to share. The share settings should be as follows:
- Link Access set to Invite Only
- Enter the email address linked with your corporate account, set the view options to "Can Contribute", then click on the Invite button.
3. If using the same computer, logout of your new Adobe account, then login to the corporate account.
4. Pick up the invitation email and click to accept.
5. Once the invitation has been accepted, open either the Lightroom desktop app or the LrWeb app using the same corporate account. You should then see, in the "Shared With You" section of the list of Shared albums, the album that you created and shared in step 2.
6. Go back to All Photos, select all the images then add them to that "shared with you" album. Make sure that you check all the share options that appear, i.e. include keywords, flags and star ratings, GPS coordinates.
7. And that's it....Lightroom will then silently copy all the images in the corporate account to your new personal account in background. I've no idea how long that will take, but it'll be a heck of a lot quicker than downloading and uploading again.
8. Of course, you've ended up with all the images in one album in your personal account, but there are (manual) things you could do. Personally, before doing step 6 I would add an album-specific keyword to all the images that are in albums (you can select all the images in an album and apply the keyword in one go, but how long that process takes you depends on how many albums you have).
Other users have used this method successfully, and I've tested it myself a few times, but worth doing it with a few images to make sure you've got all the settings correct before using it for all images.
Are you using the cloud-based Lightroom apps for iOS, Android, Windows, Mac, and Web? Then you'll love my book, 
