We report a muSR study of LiCrO2, which has a magnetic lattice made up of a stacking of triangular Heisenberg antiferromagnetic (Cr3+, S = 3/2) layers. A static magnetically ordered state is observed below the transition temperature T_N = 62 K, while the expected peak of the relaxation rate is slightly shifted downward by a few kelvins below T_N. We draw a comparison with the isostructural compound NaCrO2, where an exotic broad fluctuating regime has been observed [A. Olariu, P. Mendels, F. Bert, B. G. Ueland, P. Schiffer, R. F. Berger, and R. J. Cava, Phys. Rev. Lett. 97, 167203 (2006)] and was suggested to originate from topological excitations of the triangular lattice. Replacing Na by Li strongly narrows the exotic fluctuating regime formerly observed in NaCrO2, which we attribute to a more pronounced inter-plane coupling in LiCrO2.