Long Range (LoRa) is a wireless modulation used to provide longrange connectivity to low-power devices of the Internet of Things (IoT). LoRa gateways use hardware chips called demodulators in order to demodulate concurrent frames on different channels or spreading factors. In this paper, we establish several theoretical results on the performance of fundamental demodulator allocating strategies. In the single gateway scenario, we first prove the optimality of the basic preemptive allocation strategy. Next, in the multi-gateway scenario, the greedy non-collaborative strategy, which is currently implemented in LoRa gateways, is shown to achieve a very large approximation ratio. As an alternative, we demonstrate that a preemptive non-collaborative strategy has an approximation ratio of 2, and furthermore, that a preemptive smartcollaborative strategy reaches an approximation ratio of 3/2, for two gateways. These seminal results imply that the current performance of multi-gateway LoRa deployments can be largely improved by the proposed collaborative demodulator allocation strategies.