We present a model of Cournot rivalry where domestic and foreign firms compete in a third country market, and where the domestic export subsidy is determined by lobbying. Greater domestic cost heterogeneity (a mean-preserving spread of the marginal costs of the domestic firms) means that the subsidy level, aggregate domestic output, and domestic market share will all be higher. However, the effect of heterogeneity on domestic welfare is ambiguous. From a near symmetric initial situation, greater domestic cost-heterogeneity reduces domestic welfare if the number of domestic firms exceeds some critical value. However, when starting farther from symmetry, greater heterogeneity may raise welfare. Our results are in contrast with the nolobbying scenario, where market share is independent of increased heterogeneity, and welfare is monotonically increasing in it.