Emirates says: We pay the same price for fuel as any other airline in Dubai and in Frankfurt.
Lufthansa says: Emirates pays a low price for fuel at their hub in Dubai while we have to pay a higher price at our hub in Frankfurt. (Logically, any airline has to buy approx. 50 % of the fuel at the hub(s) and 50 % at the out stations)
The fact that Lufthansa pays the same price as Emirates for fuel in Dubai doesn't help to bring LH's fuel bill significantly down.
The fact that Emirates pays the same price as Lufthansa for fuel in Frankfurt doesn't help to bring EK's fuel bill significantly up.
I'm with EK on this one, because LH could just stop in Dubai again on the way to Asia as they had to do 20 years ago, even with full traffic rights beyond Dubai. Lufthansa Cargo or German charter airlines like Condor still frequently stop in Sharjah to stock up on cheap fuel. If Lufthansa decides to fly nonstop to Asia as a commercial decision, they should just charge a higher price to the business customers who demand the nonstop flight, and if the market doesn't accept this, then they are simply out of business on that route.