No. Lightning happens when charge builds up. When it gets big enough relative to how much resistance there is to the ground, it manages to ionize the air, creating a pathway for the charge to flow to/from ground and neutralizing it. The metal in the bullet would likely be a better conductor than air (less resistance), but it is absolutely miniscule and these things happen on an enormous scale. There would also need to be a near-critical charge there already - a lightning strike “waiting to happen”. Charge keeps building in a thunderstorm, so basically it’d just happen a moment later anyway at “best”, if you magically managed to fire a bullet at the right time and location to make a critical difference in resistance.

I don’t know about bullets, but laser beams seem to work: https://www.sci.news/physics/laser-guided-lightning-11572.html