Once you declare Mayday, you decide what you do and the controller has to accomodate you. Other aircraft not on Mayday have then to step back.
However Lufthansa was too professional to provoke such a situation, despite bad show by the controller. Rightly so.
If the captain put himself into a situation where he had to declare a mayday due to fuel he should have his four stripes stripped from his body and sacked.