From what I've read elsewhere, the laser would be a miniature, solid-state version of the Chemical Oxygen Infrared Laser (COIL) carried on the AL-1 Airborne Laser aircraft. The laser unit would be packaged in a "drop-in" turret that would take the place of the ducted lift fan located in the F-35 fuselage and would take power from the same drivetrain that powers the fan. My impression from conceptual art is that the laser turret would be steerable.
Hey, B.L.! They must not be talking chemical laser. Those won't fit on a small fixed-wing platform—that I know of (ABL takes a whole 747 to lift). I don't know lasers at all, except for the EO targeting stuff.