With all respect, I think some comments are really necessary :Note that the one with a Q of 0.7 is flat in the passband, and the one with Q of 0.8 is slightly peaked, and the one with Q of 0.6 is rolling off too soon which suggests that the general character of the low pass is being lost.
So in one case it starts to look like a sort of bandpass, and in the other case it starts to look like a defunct low pass.
This leads me to the conclusion that the idea of the Q of a filter is not always the best way to view the quality of a filter and that would apply to any kind not just low pass.
For the academic view, for a second order filter i think the lowest Q is 1/sqrt(2) before we lose the character of the low pass itself where we have a clearly defined passband and a clearly noticeable roll off.
* No, the character of a lowpass is not lost - even for Q=0.5 (which belongs to a simple RC 1st-order lowpass) we speak, of course, of a "lowpass" with a 20dB/dec roll-off
* ...looks like a "sort of bandpass" ? A 2nd-order Chebyshev lowpass (ripple w=0.5 dB) has a Q=0.864 and Q=0.956 (ripple w=1dB)
* All filter tables which are used for designing filters for 2nd and higher order filters are based (and give) Q-values for the different approximations (Butterworth, Chebyshev, Bessel, Cauer,...). Note that all the various well-known lowpass functions differ in the Q-values only!
* The quality factor Q=1/sqrt(2)=0.7071 belongs to a 2nd-order Butterworth filter - it is, of course, not the lowest possible Q value (1st-order RC-lowpass with Q=0.5)