In the embedded case, there are no self intersections, so the Mauer-Cartan equation is vacuous, and the Lagrangian is automatically unobstructed, with zero bounding cochain. The unobstructed condition is not automatic in general for immersed Lagrangians, and a significant aspect of the Joyce program in [41] is that unobstructed Lagrangians ought to be better behaved in the LMCF.