One thing we do to combat lateness (though I am in a public school) is a lockout policy. Once the bell rings, we close the door and lock it, and students must go to a central location staffed by security and assistant principals to get a pass. For every student, the number of times they are late is tallied up, and with enough tardies, students can be suspended from school.
That being said, I work in the inner city, so we have to be way harder on discipline than when I subbed in private schools. That's part of the reason I'm trying to get back there as a full-time teacher.