Yes, it is very simple and can be achieved via a normal CVD technique. Nanosheets of h-BN (III-V) are already known as white graphene due to their similar lattice structure (except of alternative B and N atoms). In this condition, the as-synthesized thin film of h-BN (already deposited on a substract) can be used for deposition of graphene layers as it is stable up to 800 C in vacuum.
Otherwise, the BN material can be mismatched to other III-V semiconducting layers!
So my question is, can we deposit graphen sheets directly on whatever semiconductors without using BN layer or we can face lattice mismatching issue in this case?
Yes, you are right. Lattice mismatch can be a big hardle. An already deposited thin film if furthe used for an other layer deposition then its top layer normally acts as a pattern. Graphen has hexagonal lattice structure whereas all the other compounds do not have the same structure. Else, the reactivity and thermal stability of III-V semiconductors also matter.