Based on the twin lamellae mechanism of crystal growth proposed by Ming and Sunagawa, the growth mechanism and kinetics of an fcc {111} crystal surface on which emerged a re-entrant corner and two types (A-type and B-type) of twin lamellae have been theoretically analyzed. Through analytical calculations we have demonstrated that the energy barrier for 2D-heterogeneous nucleation at the B-type twinned area is smaller than that for 2D-heterogeneous nucleation at a sub-step induced by a stacking fault and a re-entrant corner induced by A-type twinning, and smaller than that for conventional 2D-homogeneous nucleation making use of the first neighbour approximation. Although the nucleation barrier for 2D-heterogeneous nucleation at the re-entrant corner and also the A-type twinned area is not larger than that at the sub-step created by a stacking fault, its nucleation rate is smaller since the growth mechanism of the crystalline cluster should be considered. Our suggestion on the shape of 2D-heterogeneous nucleation is demonstrated by a Monte Carlo simulation. Thus, the twin lamellae growth mechanism is more active than the stacking fault mechanism which has been considered in our previous work.