Not so weird, really - hi and lo beams are essentially separate circuits.
I don't have my manual at hand, but don't they have separate fuses/relays for hi & lo?
Failing that, could be a wiring problem (of course) or a bad hi/lo beam switch.
then again, you might have met the little-known secret feature in 90 Accords, whereby if you perform ANY maintenance yourself (instead of going to a dealership), then the headlight low beams fail to function
