Long Range (LoRa) is a low-power wireless communication technology for long-range connectivity, extensively used in the Internet of Things. Several works in the literature have analytically characterized the performance of LoRa networks, with particular focus on scalability and reliability. However, most of the related models are limited, as they cannot account for factors that occur in practice, or make strong assumptions on how devices are deployed in the network. This article proposes an analytical model that describes the delivery ratio in a LoRa network with device-level granularity. Specifically, it considers the impact of several key factors that affect real deployments, including multiple gateways and channel variation. Therefore, the proposed model can effectively evaluate the delivery ratio in realistic network topologies, without any restrictions on device deployment or configuration. It also accurately characterizes the delivery ratio of each device in a network, as demonstrated by extensive simulations in a wide variety of conditions, including diverse networks in terms of node deployment and link-level parameter settings. The proposed model provides a level of detail that is not available in the state of the art, and it matches the simulation results within an error of a few percentage points.