If the idle speed is low it can effect the lights. If you start it on a cold morning with no choke the idle speed might be that low that a stall results with the lights glowing. The second attempt would be better especially if helped with a twist on the throttle. You might have a semi cruise control type bolt under the twist grip adjusted so that it doesn't fully retract straight away resulting in a higher idle speed on the second attempt. Hopefully that might be the case, then there is nothing wrong with your bike, apart from the relay, but I'm guessing it's got high mileage and the bearings have done a lot of work.