Nope, not a band saw. They just gum up with the soft material.
I just got off a job where we installed over 2250 TONS of lead as lead shielding for radiation.
The installers always used a chop saw to cut the bricks. I asked why they did not use a band saw, and they said they would have to keep cleaning the blade, and it would just take too long. A chop saw with a standard wood blade will cut right through the brick. I think the blade should be installed backwards for a smoother cut.
There will be some small shavings that come off the bricks, and they are a bio hazard, and should be disposed of accordingly or melted down to make an extra brick (I know you don't want to melt lead).