Velocity Factor in Transmission Line
For a lossy transmission line

\$ Z_0 = \frac{\sqrt{R+j\omega L}}{\sqrt{G + j\omega C}} 
\$

Note that for \$ R &lt;&lt; \omega L\$ and \$ G &lt;&lt; \omega C\$ this reduces to the expression in your question.

Finding the phase velocity of a lossy line is difficult as the propagation constant \$\beta \$ will, in general, be a non linear function of frequency. (Except for a distortionless line that satisfies the Heaviside Condtion). This means that the velocity factor is not a very useful metric, except over a narrow band or small distance.

In fact it means that different frequency components of a signal will travel at different speeds, resulting in distortion of the signal and inter-symbol interference in the case of digital communications.

The geometry of the cable determines the R, L, G and C parameters as well as Z and the phase velocity. 

Edit: I'm not sure if a better general expression than this can be found but the complex propagation constant will be:

\$ \gamma = j\omega \sqrt{LC}  \sqrt{1 - j(\frac{R}{\omega L} + \frac{G}{\omega C}) - \frac{RG}{\omega^2LC}}\$

Then the phase velocity is 

\$ v_p = \frac{\omega}{Imaginary(\gamma)}\$

Thus the velocity factor is 

\$ \frac{\omega}{c Imaginary(\gamma)} \$

And I don't think the Gamma expression can be decomposed into real and imaginary parts without making approximations.