Offshore oil and gas production network often comprises of one or more groups of production wells producing from different reservoir sections, with shared resources. We consider the problem of gas-lift optimization, where the lift-gas (which is a shared resource) must be optimally allocated among the wells operated by different companies. The production optimization problem with shared gas-lift resource is solved as a distributed optimization problem using Lagrangian decomposition to limit information sharing among the different subsystems and enable industrial symbiosis. However, when solving steady-state real-time optimization, a fundamental limiting factor is the steady-state wait time associated with the online model adaptation. The result is suboptimal operation during transients because we discard large chunks of transient measurement data. To address the steady-state wait time issue, we propose to update the model of each subsystem using dynamic models and transient measurements, and the distributed optimization is performed using the corresponding updated steady-state models. Using simulation results, we show that the proposed distributed RTO approach using transient measurements enable optimal resource allocation among the different subsystems.