To my mind if the F-35 can't dogfight this is not important!
USAF F-35 is the "striker" which must be protected by the F-22.
From the 20's F-35A will be an element of a huger future ("global") system with UAS/UCAV, "B-X", ISR aircraft, Spacecraft ("X-37B" style), etc.
If highly needed (to supplement the only "Increment 3.2b" 120-140 combat coded Raptors...) the F-35 could be improved (if not modified)
for the air-to-air missions with new gen AAM, engine and avionics/radar systems or... laser:
http://www.reuters.com/article/2015/04/07/us-lockheed-martin-fighter-airforce-idUSKBN0MY26Q20150407
This is just the beginning of the story and I'm sure the Lightning II hides several secrets for doghfight!