Zero and longitudinal field mu SR measurements on diluted triangular-l
attice antiferromagnet LuFeMgO4 have revealed gradual and highly aniso
tropic slowing-down of spin fluctuation. Relaxation rate lambda in the
condition with initial muon spins perpendicular to the hexagonal c-pl
ane shows divergent behavior while that in the parallel configuration
remains finite. At certain temperature range the fluctuation of spins
is suppressed by a small external magnetic field. Monte Carlo calculat
ion suggests that the correlation time for z(c)-component of spins div
erges first on cooling.