[en] $\mathrm{L}{\mathrm{a}}_{1-<!--\; ???\; -->x}\mathrm{S}{\mathrm{r}}_x\mathrm{M}\mathrm{n}{\mathrm{O}}_3/\mathrm{B}\mathrm{a}\mathrm{T}\mathrm{i}{\mathrm{O}}_3$ based multi-ferroic tunnelling junction structures promise practical on/off resistance ratio for low-field switching 4-state non-volatile memory. This work aims at investigating the nature of magnetoelectric coupling on $\mathrm{L}{\mathrm{a}}_{1-<!--\; ???\; -->x}\mathrm{S}{\mathrm{r}}_x\mathrm{M}\mathrm{n}{\mathrm{O}}_3/\mathrm{B}\mathrm{a}\mathrm{T}\mathrm{i}{\mathrm{O}}_3$ interface in the framework of density functional theory. Our results suggest that owing to electrostatic screening effect, electric polarization of $\mathrm{B}\mathrm{a}\mathrm{T}\mathrm{i}{\mathrm{O}}_3$ layer can act as the intermediary to electrically modulate not only the magnitude but also the order of local magnetic moment in $\mathrm{L}{\mathrm{a}}_{1-<!--\; ???\; -->x}\mathrm{S}{\mathrm{r}}_x\mathrm{M}\mathrm{n}{\mathrm{O}}_3$ layer. Moreover, it is demonstrated that both lateral and perpendicular strains are of particular importance to modify this kind of magnetoelectric coupling. The magnetic ordering is electrically tunable only with the application of suitable strain. (paper)