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The low-carbon operation of smart park requires to deploy massive internet of things (IoT) devices to provide real-time monitoring and control services. Digital twin (DT) provides accurate guidance for communication network resource management in low-carbon smart park by establishing a digital representation of physical entities. Facing the strict requirements of DT on delay and accuracy, as well as the constraints of access priority and energy consumption, we propose a federated learning-based DT framework and a Latency-awarE diGital twIn assisted resOurce maNagement algorithm (LEGION). LEGION can achieve a well tradeoff between delay and accuracy performances under the long-term constraints of access priority and energy consumption. Compared with existing algorithms, LEGION has superior performance in average iteration delay, DT loss function, energy consumption, and access priority deficit.