The delay was ocurred on a flight operated by UA which is neither an EU carrier nor was your flight departing from the EU. Accordingly, EC 261/2004 cancellation compensation does not apply at all.
LH would deny your claim simply on the grounds that it was not the operating carrier of the delayed flight.
Bear in mind that EC 261/2004 looks to the operating carrier only.
Although not relevant to OP's question, the rebooking responsibility here was UA's as the late-delivering carrier. Given that EWR is a UA hub, it would likely have been more fruitful to have been rerouted by UA via anu number of European destinations and then onward to DUS, hopefully arriving a good deal earlier than 24 hours late.