Artist Roberto De La Torre (The Stand) will join the Stray Bullets creator on the ongoing X-Men spinoff title.
"We're spinning out of Uncanny X-Force, so there are events in there that we directly fall out of," said Lapham at Marvel's Next Big Thing conference call.
"Basically, we open with Weapon X, who's the big bad overlord of the Age of Apocalypse world and he's just wiped out the last enclave of humanity. There's no stronghold left and there's just some scattered people around and a small resistance has to figure out what to do in these dire circumstances."
The series will focus on heroes introduced in Marvel's Point One anthology - alternate reality versions of some of the X-Men's greatest human foes, including William Stryker, Donald Pierce and Graydon Creed.
"They're the same people but they grew up in an entirely different world under entirely different circumstances," said Lapham.
The Age of Apocalypse is an alternate reality that was introduced during the X-Men crossover of the same name in the mid-'90s.
It was reintroduced in the pages of Rick Remender's Uncanny X-Force.
Age of Apocalypse #1 will debut in March, 2012.