Augmenting the long-term evolution (LTE)-evolved NodeB (eNB) with cloud resources offers a low-latency, resilient, and LTE-aware environment for offloading the Internet of Things (IoT) services and applications. By means of devices memory replication, the IoT applications deployed at an LTE-integrated edge cloud can scale its computing and storage requirements to support different resource-intensive service offerings. Despite this potential, the massive number of IoT devices limits the LTE edge cloud responsiveness as the LTE radio interface becomes the major bottleneck given the unscalability of its uplink access and data transfer procedures to support a large number of devices that simultaneously replicate their memory objects with the LTE edge cloud. We propose Replisom ; an LTE-aware edge cloud architecture and an LTE-optimized memory replication protocol which relaxes the LTE bottlenecks by a delay and radio resource-efficient memory replication protocol based on the device-to-device communication technology and the sparse recovery in the theory of compressed sampling. Replisom effectively schedules the memory replication occasions to resolve contentions for the radio resources as a large number of devices simultaneously transmit their memory replicas. Our analysis and numerical evaluation suggest that this system has significant potential in reducing the delay, energy consumption, and cost for cloud offloading of IoT applications given the massive number of devices with tiny memory sizes.