We present here a model for the non-Born-Oppenheimer description of the biexcitonic complex X2(eehh) trapped in laterally-coupled quantum dot system. We define a zeroth-order Hamiltonian which allows us, under certain conditions on the masses and coupling constants, to decouple the problem. We show that the zeroth-order wavefunctions and energies can be described using the exact solutions for the Hookean model for the H2 molecule [Ludeña et al., J Chem Phys 2005, 123, 024102]. We also apply this Hookean model to the description of the excitonic complexes X+2 (ehh), X-(eeh), and to the single exciton X(eh) and analyze the dependence of the total non-Born-Oppenheimer zeroth-order energies, and binding energies for these sytems with the mass ratio α. The general features of the results obtained using this Hookean model agree quite well with those of more elaborate calculations.