When the tech remoted in, they said that I did not have Lucida installed
Impossible. If Lucida Grande is not installed, OS X won't even start up. Font Book will not let you trash that font. Not even if you select, tell it to remove the font, and confirm. It still will not move to the Trash. The only way to get it there is to manually delete it from the /System/Library/Fonts/ folder. And even if you do that, it will immediately be replaced by a copy of the font buried deep in the system. Certain fonts are protected that way.
The three most likely causes are:
1) A corrupt font (or more than one)
2) A corrupt database (common, and commonly caused by corrupt fonts)
3) A corrupt font collection.
Try dealing with 2 and 3 first. For the second possible issue, do this:
Close all running applications. From an administrator account, open the Terminal app and enter the following command. You can also copy/paste it from here into the Terminal window:
sudo atsutil databases -remove
Terminal will then ask for your admin password. As you type, it will not show anything, so be sure to enter it correctly.
This removes all font cache files. Both for the system and the current user font cache files. After running the command, close Terminal and immediately restart your Mac.
If that doesn't do it, then remove the font collections. They are in your user account. To get there, first be at the desktop. Then hold down the Command key and choose Go > Library from the menu. Your user account Library folder will open. Within that, open the FontCollections folder and move all items in there to the desktop. Try launching Font Book again.