The Terahertz (0.1-10 THz) band has been envisioned as one of the promising spectrum bands to support ultra-broadband sixth-generation (6G) and beyond communications. In this paper, a wideband channel measurement campaign in a 500- square-meter indoor lobby at 306-321 GHz is presented. The measurement system consists of a vector network analyzer (VNA)-based channel sounder, and a directional antenna equipped at the receiver to resolve multi-path components (MPCs) in the angular domain. In particular, 21 positions and 3780 channel impulse responses (CIRs) are measured in the lobby, including the line-of-sight (LoS), non-line-of-sight (NLoS) and obstructed-line-of-sight (OLoS) cases. The multi-path characteristics are summarized as follows. First, the main scatterers in the lobby include the glass, the pillar, and the LED screen. Second, best direction and omni-directional path losses are analyzed. Compared with the close-in path loss model, the optimal path loss offset in the alpha-beta path loss model exceeds 86 dB in the LoS case, and accordingly, the exponent decreases to 1.57 and below. Third, more than 10 clusters are observed in OLoS and NLoS cases, compared to 2.17 clusters on average in the LoS case. Fourth, the average power dispersion of MPCs is smaller in both temporal and angular domains in the LoS case, compared with the NLoS and OLoS counterparts. Finally, in contrast to hallway scenarios measured in previous works at the same frequency band, the lobby which is larger in dimension and square in shape, features larger path losses and smaller delay and angular spreads.