A machine for intended use in feeding and completing partially formed cartons is disclosed. In one embodiment, the machine includes an overhead conveyor with selectively actuated, depending lugs that engage and convey the carton in a first direction while a first flap on a lid is folded and sealed. A takeaway conveyor includes selectively actuated, upstanding lugs that convey the carton in a second direction generally perpendicular to the first direction while second and third flaps are folded and sealed. The lugs on each conveyor may be closely spaced or overlapping to allow for selective actuation at a desired instant in time without the need for timing the corresponding chain or the carton feed. A diverter located at a transition between the forward and return runs of the overhead and takeaway conveyors actuates the lugs in a controlled fashion. Related methods of feeding and forming cartons are also disclosed.