How do you calculate the lookback time distance to a given galaxy?

No you can't. Other information is required.

For low redshifts - let's say smaller than 0.1 - and by that I mean the wavelength increases by 10 percent, you might get away with using Hubble's law to estimate the distance and then get the look back time by dividing by the speed of light.
$$ t simeq frac{lambda - lambda_0}{H_0 lambda_0},$$
where $H_0$ is the present day Hubble parameter of about 70 km/s per Mpc, $lambda$ is the measured wavelength and $lambda_0$ is the rest wavelength.

So far so good, you just need to know $H_0$. However for larger redshifts it gets horribly complicated because the Hubble parameter changes with time in a way that depends on the curvature of the Universe and hence on the cosmological parameters defining the matter density and dark energy density.

There is indeed a highly complicated, non- linear formula involving integrals that I will look up a reference for. But possibly the better way to proceed is to use a simple look-up table produced from such calculations with certain assumed values for ratios of matter and dark energy densities with respect to the critical density; a.k.a. $Omega_M$ and $Omega_{Lambda}$.

The plot below is an example taken from http://www.astro.caltech.edu/~eran/MATLAB/Cosmology.html which shows look back time versus redshift for two different cosmologial models (but with the same value of $H_0$). The curves are very different at high redshifts, but converge at small redshifts.

Here is a cosmological calculator that can do the job for you. Enter the redshift and your assumptions about the Hubble parameter and other cosmological parameter and it will tell you the age of the universe at that redshift as well as the lookback time.