There are two relays on the right side and three relays on the left;
the one that feeds the headlights is on the right side;
of the two relays. one has three wires - this is the Turn Signal Relay;
the other is the headlight/starter Relay;
the headlight/starter relay receives power from Fuse 9 on the Blue/Yellow wire when the key-switch is on;
it outputs through the Normally Closed Terminal on the Blue wire o the headlight circuit when the relay is unenergized;
When the relay turns on (when the starter switch is operated) it transfers power through the normally open contact via the black wire to the starter solenoid and fires the starter, simultaneously breaking power to the headlight circuit.
If bike is starting you therefor MUST have power through the key-switch and fuse 9 and the relay is functioning with the starter switch to transfer that power to the starter.
It is possible there is a burned connection on the normally closed contact of the relay - or the Blue Wire is broken;
so check for 12V at the Blue wire (this will be the centre pin of the 5 of the relay) - note that key-switch must be on and the relay must be installed.
The other conceivable issue is that this location has the wrong relay installed - this one MUST be a 5-pin relay - if you have a 4-pin in that position then indeed starter would operate normally but you have no lights.
If you DO have 12V at the blue wire, that then goes to the connector that goes to the Left Switch assembly - is Blue on pin 10 at the main harness side, switches to Blue/Yellow on the side going up to the switch.
Check the connector set for either burned terminals or broken wires (or simply unplugged - sometimes the latch that locks them together gets broken)