2008 suzuki gsx-r low beam headlight won't come on

High beam switch moat likely, have you checked relays and fuses?

Someone would need to check for voltage output on the dimmer switch for low and high beam.

There is a headlight relay in the engine compartment fuse box, but its after the headlight switch and before the dimmer switch, so it powers both high and low beam circuits.
I would check the dimmer switch.

change the headlight bulb

Low beam switch may be bad. use a meter to check for power to lowbeam side of lamp. cleaning with electrical contact spray may help.

does high beam work? if it does, then maybe its just a blown low beam filament. if it doesn't and the fuse is good... then check for loose connections or corroded pins going to the light assembly socket.

Sounds like your low beam relay isn't working, try swapping it with the high beam relay to see if it cures, if it does pop down to a Suzuki dealer to get yourself a new one, if it doesn't then check all the connections in between switchgear and relay, relay and headlight for corrosion.

more than likely it is nothing more than a blown low beam fillament in the globe apart from that the system may be fused on both high & low beam however Im not to sure about that on this model

yes this is correct