Li2MnO3 with a S=3/2 two-dimensional Mn honeycomb lattice has a Neel-type antiferromagnetic transition at TN=36 K with a broad maximum in the magnetic susceptibility at TM=48 K. We have investigated site percolation effects by replacing Mn with nonmagnetic Ti, and completed a full phase diagram of Li2Mn1-xTixO3 solid solution systems to find that the antiferromagnetic transition is suppressed continuously without a clear sign of changes in the Neel-type antiferromagnetic structure. The magnetic ordering eventually disappears at a critical concentration of xc=0.7. This experimental observation is consistent with percolation theories for a honeycomb lattice when one considers up to 3rd nearest-neighbor interactions. This study highlights the importance of interaction beyond nearest neighbors even for Mn element with relative localized 3d electrons in the honeycomb lattice. ; Comment: 6 figures, 1 table J. Phys. Condensed Matter (accepted)