So would that mean no compensation if QF10 (LHR-DXB) arrives over 3 hours late?
Some months ago (though not in identical circumstances) we had a discussion on AFF about whether EU compensation would be payable; one aviator disagreed with others so in the end it was indeterminate.
This otherwise quite extensive guide does not mention 'medical diversions' as an 'extraordinary circumstance' but my assumption is that QF would suggest that it was such an occasion and hence not offer compensation:
How to claim EU flight delay compensation|(EC) 261/2004 | This is Money
This source however suggests that a medical diversion would qualify as an 'extraordinary circumstance' and hence compensation would not be payable by an airline:
https://www.flightdelays.co.uk/extraordinary-circumstances
One might try to obtain a statement in writing from QF as to the exact cause of the delay, preferably from check in, lounge or gate staff, and then lodge a claim (keeping a copy) with QF and see what occurs. You could also ask at the gate as to whether the QF staff were distributing information about claiming EU compensation.
Independently, upon your return to your destination, you could contact staff at LNC airport to seek their understanding as to what exactly caused the delay. They might even email you the reason if you came into contact with a kind individual.
One other factor you could highlight is that prior to the diversion to Lanarca, Cyprus, QF1 was already hours late as it had not departed DXB until 0602 hours this morning. See my post number 5646 above. Note however that what was at that stage an expected arrival of 1025 hours in LHR would not have by itself meant a three hour plus delay to QF10, but since it shows evidence of an inbound delay that may be the airline's fault as defined in the EC regulation, it might be a point worth making.
UPDATE: QF1 departed LNC at 1158 hours. LHR predicted arrival has become later at around 1455, meaning that QF10 will be unable to depart much before 1640 hours - three hours and 10 minutes late, but once again, that estimate is reliant on everything going well and ATC giving clearance for a prompt departure at a busy time of the afternoon to an aircraft that ought have been off blocks a significant time previously if the timetable was being adhered to.
This will mean that the Wednesday evening 12 July 2255 hours MEL - DXB - LHR will depart late. Just how much will be unknown until DXB departure in many hours' time, but at least passengers who view AFF have more than 24 hours' warning of the delay.