Hi JoeNova,
The lowest rate you can resolve will depend heavily on how well you control other system parameters. Supply voltage and temperature changes, among other factors, will have a large effect, as will any vibration in the structure.
A measure of the absolute best accuracy you could ever achieve with a gyro is given by the Allan Deviation chart. For the ADXRS624 you can find this chart on page 8 (Figure 18) of the datasheet. The null bias stability is read at the minimum of that curve, so the plot suggests that the very best you can do -- assuming all other error sources are eliminated completely -- is 0.006°/s.
HOWEVER --
Take a look now at Figure 5, which shows a histogram of measured null drift over temperature. A typical value might be 0.05°/s/°C. If you are trying to achieve a stability much better than 0.006°C, you would have to be able to control your temperature down to much better than 0.12°C. Maybe >10x better, for this to be negligible by comparison.
You can perform a similar calculation for the error induced by variations in supply voltage and linear acceleration and you will see that these all add up to a much higher "lowest resolvable rate" than what you get from the Allan deviation curve.
All this verbiage to illustrate that there is no number we can give you in a datasheet that will tell you the lowest rate you can measure in your application, because the most significant error sources will come from the system and its environment, not from the gyro itself.
I hope this helps!
Nitzan