Just a guess as a non-expert: the higher the rotation rates, the wider the spacing between the clockwise and counterclockwise beams (or modes), and hence the harder it will become to change this wavelength. Note that in a laser you need to fullfill the cavity roundtrip condition, which means that you need more or less an integer number of wavelengths per roundtrip. Slight deviations are allowed (finite linewidths), but these cannot become too large.
Lasers do not have a THz frequency range. This is an ill-defined statement. There is a free-spectral range, there is an optical linewidth, and there is a gain bandwidth. You will have to be more specific.
Ring laser gyro has two beams travelling in clockwise and counterclockwise direction.At very low rotation rates,the frequencies of these two beams becomes almost identical so they tend to undergo locking mechanism.
This makes change in frequency to be zero..
For analytical details u can refer the link provided..
I have limited experience with ring laser gyros, but I believe that the suggestions cited in prior answers is correct: as the rotation rate increases the frequencies of the two beams (clockwise and counterclockwise) diverges to the point that locking becomes more difficult.