Adiabatic lapse rate is defined as $$ \Gamma_a \equiv -\left(\frac{dT}{dz}\right)_{\rm parcel}=-\frac{R_{\rm a} T}{c_p \,p}\left(\frac{dp}{dz}\right)_{\rm parcel} = \frac{g}{c_p} $$ $R_a$ is gas consntant divided by molar mass. If I have a parcel of dry air, I have dry adiabatic lapse rate.
Now, for standard atmosphere, I do not have $p(z)$ but I have $T(p)$ (in form of point data). Neither have I $c_p(p)$ and neither $g(p)$ and neither. So my idea to get the adiabatic lapse rate in general is: $$ -\left(\frac{dT}{dz}\right)_{\rm parcel}=-\left(\frac{dT}{dp}\right)_{\rm parcel}\left(\frac{dp}{dz}\right)_{\rm parcel}=\left(\frac{\Delta T}{\Delta p}\right)_{\rm parcel} \rho g=\left(\frac{\Delta T}{\Delta p}\right)_{\rm parcel} \frac{p}{R_a T} g $$ Is this a correct approach?
Now to get dry adiabatic lapse rate I have absolutely no idea how to approach that because of I do not know $c_p(p)_{\rm dry-air}$ and neither e.g. $g(p)$. The only thing I know is the molar mass of dry air. Are those data about $T(p)$ for the atmosphere of any use for dry adiabatic lapse rate? What relations am I missing?