Different application. Plywood is flat sheets, LVL is dimensional lumber like a 2x4, etc. Plywood is laid up with different grain orientations from ply to ply to optimize shear strength. LVL is, I presume, all with grain in the same direction, optimizing tensile and bending strength.Why not just use aircraft grade plywood? It has well documented properties.
And, as mcrae0104 said, LVL will probably be heavy for the strength.