The Lomb-Scargle method produces a periodogram, i.e., powers at each frequency. This is in order to be able to be performant, compared to directly least-squares fitting a sinusoidal model. I don't know about gatspy, but astropy does allow you to compute the best phase for a specific frequency of interest, see http://docs.astropy.org/en/stable/stats/lombscargle.html#the-lomb-scargle-model . I imagine doing this for many frequencies is many times slower than computing the periodogram.

-EDIT-

The docs outline moved to: https://docs.astropy.org/en/stable/timeseries/lombscargle.html