In this paper, we present new closed form expressions for lower bounds on the end-to-end outage probability of a dual-hop, non-regenerative cooperative communication system over independent, not necessarily identically distributed, gamma-shadowed Nakagami-m fading channel. More specifically, we obtain new closed form expressions (in terms of Meijer's G function) for the cumulative distribution function (CDF) on the upper bound of the end-to-end signal-to-noise ratio (SNR) and the end-to-end signal to interference ratio (SIR) of the above cooperative communication system and then use these expressions to evaluate the lower bounds on the outage probability for both noise-limited and interference-limited cooperative communication systems. Finally, numerical plots illustrate the presented mathematical analysis.