We study the gluon and ghost propagators of SU(2) lattice Landau gauge theory and find their low-momentum behavior being sensitive to the lowest non-trivial eigenvalue (lambda_1) of the Faddeev-Popov operator. If the gauge-fixing favors Gribov copies with small (large) values for lambda_1 both the ghost dressing function and the gluon propagator get enhanced (suppressed) at low momentum. For larger momenta no dependence on Gribov copies is seen. We compare our lattice data to the corresponding (decoupling) solutions from the DSE/FRGE study of Fischer, Maas and Pawlowski [Annals Phys. 324 (2009) 2408] and find qualitatively good agreement.