The development of spin glass like state in a geometrically frustrated (GF) magnet is a matter of great debate. We investigated the effect of magnetic (Mn) and nonmagnetic (Ga) doping at the Cr site of the layered GF antiferromagnetic compound LiCrO2. 10% Ga doping at the Cr site does not invoke any metastability typical of a glassy magnetic state. However, similar amount of Mn doping certainly drives the system to a spin glass state which is particularly evident from the relaxation, magnetic memory and heat capacity studies. The onset of glassy state in 10% Mn doped sample is of reentrant type developing out of higher temperature antiferromagnetic state. The spin glass state in the Mn-doped sample shows a true reentry with the complete disappearance of the antiferromagnetic phase below the spin glass transition. Mn doping at the Cr site can invoke random ferromagnetic Cr-Mn bonds in the otherwise 120 degree antiferromagnetic triangular lattice leading to the non-ergodic spin frozen state. The lack of spin glass state on Ga doping indicates the importance of random ferromagnetic/antiferromagnetic bonds for the glassy ground state in LiCrO2. Spin glass state in GF system has been earlier observed even for small non-magnetic disorder, and our result indicates that the issue is quite nontrivial and depends strongly on the material system concerned.