The base of the bullet is lead (with jacketed pistol rounds, that's often true even if it's a "full metal jacket" and some brands are trying to draw a distinction there with "total metal jacket" branding) and it's exposed to the explosion when the round fires. There's some vaporized lead, most if it will move downrange and some of it won't. Airborne lead is potentially more of a problem at an indoor range.

Copper, polymer-coated, or total metal jacket rounds will also result in less lead on the firearm, I'd think, and less on the user's hands. One old guy I know who had lead poisoning at one time believes the real risk is getting the lead on one's hands and then handling a cigarette.