A lot of works have been done to demonstrate that buffer-aided relaying can achieve a significant performance gain in cooperative wireless networks. However, the additional delay introduced by buffer has been largely neglected in available works, which is of significant importance for delay-sensitive networks. In this paper, we consider a two-hop buffer-aided relaying system suffering from eavesdropping, where every packet owns a limited lifetime. In order to satisfy a specific secrecy rate of the system, this paper proposes a novel security and lifetime (SELI)-aware relay selection scheme by balancing the security and lifetime constraints. Furthermore, to address the problem of the heterogeneous packets queuing in the buffer, the approach of Markov chain is embedded to model the packet occupancy process. With the help of this complete framework, we derive the exact expressions of performance metrics, including reliable outage probability, packet discarding probability and secrecy throughput. Finally, extensive simulation and numerical results are provided to validate our analysis and illustrate the proposed scheme can efficiently reduce the packet discarding ratio.