Reasoning about concurrent programs executed on weak memory models is an inherently complex task. So far, existing proof calculi for weak memory models only cover safety properties. In this paper, we provide the first proof calculus for reasoning about liveness. Our proof calculus is based on Manna and Pnueli’s proof rules for response under weak fairness, formulated in linear temporal logic. Our extension includes the incorporation of memory fairness into rules as well as the usage of ranking functions defined over weak memory state. We have applied our reasoning technique to the Ticket lock algorithm and have proved it to guarantee starvation freedom under memory models Release-Acquire and Strong Coherence for any number of concurrent threads.