Motivated by manufacturing and service applications, we consider a single class multi-server queueing system working under the LCFS discipline of service. After entering the queue, a customer will wait a random length of time for service to begin. If service has not begun by this time she will abandon and be lost. For the GI/GI/s+M queue, we present some structural results to describe the relation between various performance measures and the scheduling policies. We next consider the LCFS M/M/s+M queue and focus on deriving new results for the virtual waiting time and the sojourn time in the queue (either before service or before abandonment). We provide an exact analysis using Laplace-Stieltjes transforms. We also conduct some numerical analysis to illustrate the impact of customer impatience and the discipline of service on performance.