The current medium access in LoRa, involving strategies very similar to early ALOHA systems, does not scale for future denser LoRa networks, subject to many collisions. Semtech's Channel Activity Detection (CAD) feature enables to implement a carrier sense (CS) in LoRa WANs, but its unreliability at short distance dramatically decreases its efficiency for classical CS strategies. We present CANL, a novel LoRa channel access approach based on an asynchronous collision avoidance (CA) mechanism and operating without the CAD procedure. Extensive simulations using an extended LoRaSim confirm the performance of CANL in a wide range of configurations. The results are promising and show that the proposed CA approach can greatly increase the delivery ratio in dense LoRa networks compared to a classical CS strategy while keeping the energy consumption at a reasonable level.