This paper considers a single vendor-single buyer coordinated supply chain under stochastic demand. GHG emissions arise from the vendor's production process. A carbon tax and penalties for exceeding multiple emissions limits are considered. A random number of defectives characterises the batch received by the buyer, who performs an inspection activity. Setup and transportation times are controllable through a capital investment, whose outcome is uncertain. An optimisation problem is formulated under the minimax distribution-free approach. The objective is to find the production-inventory replenishment policy and the length of setup and transportation times that minimise the long-run expected total system cost rate considering a fill rate constraint. Several properties of the cost function are demonstrated, and an optimisation method is developed. Finally, numerical experiments are carried out to draw insights on the effect of the model parameters, including different legislation schemes concerning GHG emissions, on the optimal system performance. The novelty of the paper consists into investigating the effect of a controllable lead time on coordinated supply chain decisions in presence of GHG emissions and quality issues, in a stochastic environment. A major finding is that controlling lead time enhances both the overall cost efficiency and the environmental sustainability of the system.