We investigate the cross spectrum of XTE J1701-462 in various types of neutron star low-mass X-ray binary subclasses during its 2006-2007 outburst. We analyze the relation between the time lags and temporal variabilities. We find that the hard time lags accompany horizontal branch oscillations (HBOs) and the soft time lags dominate the noise in the low frequency range 0.1-10 Hz on HB. In the Cyg-like phase, the time lags decrease on the middle normal branch (NB) from HB/NB vertex to NB/FB vertex, whereas the time lags are roughly invariant in the Sco-like source. We discuss the fact that the Compton upscattering by the corona introduces the soft lag in low-frequency noise. We suggest that the variation of the Comptonization component from the disk emission leads to the HBOs' time lag evolutions along the Z tracks. We also report the rms amplitude spectrum and phase lag spectrum for the normal branch oscillation (NBO). A similar to 160 degrees. phase lag is found. We find that the rms amplitudes of both the Cyg-like and the Sco-like NBOs linearly increase with the photon energy in low energy bands, and drop in the highest energy band.