Long Range (LoRa) technology constitutes one of the major enablers of future Internet-of-Things (IoT) applications, such as monitoring of challenged environments and smart buildings. However, crucial issues in the context of multi-gateway LoRa networks have been overlooked. In particular, most existing methods did not consider the stringent constraint of limited number of demodulators at each gateway. Therefore, we devise a gateway selection method for uplink LoRa transmissions, where this limited availability of demodulators is fully considered. We propose an optimization approach based on the auction mechanism, where each IoT device is pre-assigned to a unique gateway, so as to maximize the total amount of demodulated transmissions without redundancy at the network server. Furthermore, a low complexity method is also designed, where devices are partitioned into groups and where auctions are parallelized. Numerical results show that the proposed methods largely outperform benchmark algorithms in terms of the network utility function and sum-rate, while approaching the upper bound performance. The proposed methods are particularly suited to cope with the inherent dynamics of mobile LoRa IoT networks, as highest gains are attained for demodulation latencies in the order of tens to hundreds of milliseconds.