Interfaces are inarguably the most significant micro-structural features that impart extraordinary mechanical properties to nanolamellar alloys. Since lamellar alloys have a variety of compositions and heat treatment methods, they can exhibit different kinds of interfaces. Every individual interface plays its own specific role during deformation which is difficult to isolate, owing to the inherent lamellar morphology. For instance coherency stresses and misfit dislocations at the interfaces individually influence the plastic behaviour, but such effects are superimposed in the lamellae and difficult to isolate in experiments. In this work, however, we employ atomistic modeling to accurately model isolated coherent and semi-coherent interfaces in two phase lamellar TiAl and thereby decouple their individual effects on the deformation behavior. In detail, we study the tensile behaviour of $\alpha_2/\gamma$ (DO$_{19}$/L1$_{0}$) and $\gamma/\gamma$ (L1$_0$/L1$_0$) interfaces modeled as  bi-crystals. The $\alpha_2/\gamma$ interface is akin to $hcp/fcc$ and the inherent lattice misfit, either causes severe coherency stresses, or misfit dislocations in the system. Both scenarios are replicated. Using this we explore the origins of early yielding due to microplasticity in lamellar alloys. Similarly, a $\gamma/\gamma$ interface is akin to a $fcc/fcc$ (111) twin boundary, but the tetragonality of the $\gamma$ phase creates a small lattice mismatch, and thus the conditions for coherency stresses and misfit dislocations as well. We compare this system with a coherent twin boundary that is devoid of coherency stress with a system with coherent or semi-coherent twin boundaries exhibiting coherency stresses and explore, in atomistic detail, the possible deformation mechanisms arising due to different interface types.