Batman's cowl being lined with lead has been mentioned in Post-Crisis issues such as Superman/Batman Annual #1 and Superman/Batman #9. Seemed to be presented as standard gear in those issues, rather than something worn for specific missions.
SUPERMAN: I have super-hearing, you know... I can hear the wheels turning in your brain. Figure it out yet?
BATMAN: I've read the "who's who" of every college from the last twenty years. I'll find that chin one of these days. And you...?
SUPERMAN: Nope. Lead lining in the cowl was a good idea, but honestly, I'm way too busy to figure you out.
Superman/Batman Annual #1 (December, 2006)
SUPERGIRL: Why do you wear eyeglasses if you can see better than anyone on the planet?
SUPERMAN: When those of use who are... heroes want to have lives without the cape, it's important to keep our identities a secret.
SUPERGIRL: And that's why Batman doesn't take off his lead-lined cowl?
SUPERMAN: You noticed the lead, hmm? I didn't know your x-ray vision had kicked in.
SUPERGIRL: You didn't ask.
Superman/Batman #9 (June, 2004)
Jean-Paul Valley's Batman mask was also stated to be lead-lined in World's Finest Vol. 3 #9.
SUPERMAN: Sorry. It's been a while, hasn't it? First I was dead, then Bane broke you -- at least, that's what I heard. Nice to see you're back on your feet. I like your new look -- especially the lead-lined mask.
World's Finest Vol. 3 #9 (December, 1999)
Batman was known to use lead lining in his masks in some Pre-Crisis stories, however in these cases it didn't appear to be standard gear.
For example, in Detective Comics Vol. 1 #327, he used lead lining in his mask to shield his brain from a device a villain had previously used to paralyse him. Evidently, the lead lining wasn't present in the earlier instance, otherwise the device wouldn't have worked on him the first time.
BATMAN: Before you go, Fenton... Robin and I deduced that you planted those marks on our foreheads with a beam of radioactive phosphorus! And we realized afterward that the invisible imprint of that beam on us enabled you to send out and energy signal -- from this box in your pocket -- which affected the motor areas of our brains -- so that anytime you wanted, within a range of about ten feet, you could halt us -- stop us from moving!
FRANK FENTON: Yeah, Batman, but how...?
BATMAN: How did we outwit you? With a lead lining inside my mask that prevented your energy signal from reaching me!
Detective Comics Vol. 1 #327 (May, 1964)
While under hypnosis from Superman in World's Finest Vol. 1 #155, Batman also modified one of his costumes in various ways -- including lining the mask with lead -- so that he could assume the alter-ego of Nightman. Again, this suggests his masks weren't lined with lead as standard.
ROBIN: But you made us all think you didn't know who Nightman was!
SUPERMAN: But I never said I didn't know... I'd given Batman an hypnotic command to line his mask with lead, so I couldn't truly say that I could see Nightman's face!
World's Finest Vol. 1 #155 (February, 1966)