Symmetry-adapted perturbation theory (SAPT) expansions corresponding to several symmetry-forcing procedures are applied through large order to study the interaction of lithium and hydrogen atoms. The interaction energies predicted by the perturbation theory are compared with the results obtained using the full configuration interaction (FCI) method. Since the ground state of the LiH molecule is submerged in the continuum of Pauli-forbidden states, these calculations are a demanding test for the SAPT approach in which the electrons from different monomers are treated as distinguishable particles. We show that if the symmetry is forced in a rather weak way, characteristic of the Murrell-Shaw-Musher-Amos theory, a divergent perturbation series is obtained. When the symmetry is forced in a strong way, as is done in the Eisenschitz-London-Hirschfelder-van der Avoird theory, one obtains a convergent series, but the interaction energy computed through any finite order exhibits wrong asymptotic behavior at large interatomic distances R. We show that by forcing the symmetry in an appropriate, intermediate way one obtains perturbation series which correctly predict leading terms in the 1/R asymptotic expansion of the interaction energy and, despite the presence of the Pauli-forbidden continuum, converge quickly to the FCI value of the interaction energy.