Because LucidChart files are actually stored within the Lucidchart file system, you will need to move your Lucidchart files over to your new account.
Log into your @ucsd.edu Google MyDrive - please use a separate Chrome Profile, or at least an incognito tab for this (to keep it separate from your @eng.ucsd.edu Google account)
Click New > More > Lucidchart - and activate your new account
Now, in your separate window where you're logged in as @eng.ucsd.edu Google account, go to https://lucid.app/documents#/documents?folder_id=home . This will show you all of your Lucidchart files.
@eng.ucsd.edu - Right-click on "Team Folders" > New Team Folder - you can call it username-transfer (where username is your username)
@eng.ucsd.edu - Right-click username-transfer > Share > type in your @ucsd.edu Google account address, choose Edit and Share, uncheck Notify via email, and click Invite
@eng.ucsd.edu - Click on My Documents, highlight the first file in the list, hold down your shift key, and highlight the last file in the list - this will highlight all of your Lucidchart files
@eng.ucsd.edu - Drag your highlighted files into the username-transfer folder - click Move after reading the warning
@ucsd.edu - Now, go back to your @ucsd.edu Google window, and if you're not already there, open https://lucid.app/documents#/documents?folder_id=home in that window
@ucsd.edu - click on Team Folders > username-transfer
@ucsd.edu - You will see your Lucidchart files there - highlight all the files here, and Drag the highlighted files into "My Documents"
Transfer is now complete.
NOTE: If others have shared Lucidchart files with you, and you need to keep the files, you can either reopen those files from whatever link you were originally sent, and ask for permission - OR if you just need to retain a copy for your records, you can right-click on the file in "Shared with me", choose Duplicate, and then move that copy over to your new account per the method above.