A free-space optical communication system using non-mode-selective photonic lantern (PL) based coherent receiver is studied. Based on the simulation of photon distribution, the power distribution at the single-mode fiber end of the PL is quantitatively described as a truncated Gaussian distribution over a simplex. The signal-to-noise ratios (SNRs) for the communication system using PL based receiver are analyzed using different combining techniques, including selection combining (SC), equal-gain combining (EGC), and maximal-ratio combining (MRC). The integral solution, series lower bound solution and asymptotic solution are presented for bit-error rate (BER) of PL based receiver, single-mode fiber receiver and multimode fiber receiver over the Gamma-Gamma atmosphere turbulence channels. We demonstrate that the power distribution of the PL has no effect on the SNR and BER performance of the PL based receiver when MRC is used; and it only has limited influence when EGC is used. However, the power distribution of the PL can greatly affect the BER performance when SC is used. Besides, the SNR gains of the PL based receiver using EGC over single-mode fiber receiver and multimode fiber receiver are numerically studied under different imperfect device parameters; and the scope of application of the communication system is further provided.