It sounds like Travelocity might have been in error. The Lufthansa website makes it clear that any changes should have been handled by your agent, and not by Lufthansa. 'Economy Basic' fares seem to attract a handling charge of either �25 or �50 from Lufthansa. (However, an agent would be entitled to add on their own administration fee. Travelocity's fee for any changes is �45). I can see nothing on the Lufthansa website to indicate that no changes are permitted to even their cheapest tickets. However, the bad news is that, if you've purchased Economy Basic tickets, absolutely no refunds are permitted.
It is, of course, possible that Lufthansa made some extra-cheap tickets available through Travelocity, with a 'no changes' rule applied to them. If so, that rule should have been shown (either directly or by clicking on a relevant link) at the time of purchase. Check what it says on the tickets. If 'Economy Basic' or 'Economy Flex' is shown. it's likely that a change could have been made (for the fees indicated above). However, if 'Discount', 'Economy Special' or something similar appears, then you were given the chance to view the rules and you've no right to complain when those rules are applied.
Travelocity is part of the same (American-owned) group which includes LastMinute.com. They've generally got a good reputation in terms of customer service. Query their decision. If they're in error, they'll probably admit it and offer you some compensation but you can't expect them to pay you anything if you simply didn't read the rules at the time of booking. Write to Customer Relations Department, 4th Floor Victoria Gate, Chobham Road, Woking, Surrey, GU21 6JD.
Chris