We propose a symmetry-based method of using noncentrosymmetric optical lattices to systematically control topological nontrivial orbital hybridization. A crucial difference from the previous studies is the role of inversion symmetry breaking, which is applied to induce an exotic orbital-changing hopping perpendicular to the direction without inversion symmetry and opens a band gap, instead of reducing the codimension and producing gapless points. The orbital mixing here is reminiscent of the spin-orbit physics based on hyperfine states but differs in symmetry and origin. This nontrivial orbital hybridization produces a topological band structure. Attractively interacting fermionic atoms loaded in such a lattice are found to show an orbital topological Fulde-Ferrell superfluid state in the presence of onsite rotation. This state supports Majorana fermions on its edges. Our mechanism should pave an alternative way to achieve orbital topological phases in optical lattices of nonstandard geometry.