LH, like many other airlines, has a number of special offers "no changes, no refunds( other than taxes and charges)" and it soulds like you've bought one of these.... so the first answer is hard "if it is cheap, there is bound to be snag
"
Talking to some hot line means that you get somebody with a list of faqs and the answers - whcih is why I call such things "The Unhelp Desk
"...
Your travel agent, or your company travel agent, has a contact for a LH Agency Service Centre where one can get intelligent help - but first do a litle research and see what offers you can find in Business with one of the major carriers, and then pop the question about upgrading.
Good luck!
Pteropsid