Hi
what type of exercises are you doing? You maybe over breathing/over doing it which can cause the lightheaded feeling which in turn the bodies natural reaction is to try and lie you down to return to normal carbon/oxygen levels. I read on a site about hyperventalation which is when you over breath which upsets the bodies carbon/oxygen levels, good news is, is that if you were going to pass out you would have after the first episode. Next time when you are down the gym, take it easier and see if that helps. If it doesn't make any difference to your symptons, report your problem to the doctor and have a minor heart/lung check up.
Let us know how you get on.