The large-scale use of natural gas units intensifies the interactions between power grid (PG) and natural gas network (NGN), which puts forward new requirements for the expansion planning for PG and NGN. Existing planning methods have high redundancy to cope with the uncertainty in the long-range year. To solve it, this paper proposes a joint dynamic planning method for grid and gas network with the integration goals of economic, reliable and low-carbon from the lifecycle perspective. A lifecycle cost management model for electricity lines and natural gas pipelines is established using a lifecycle management approach, including construction, operation, retirement, environmental, and load curt costs. A joint planning model of PG and NGN is proposed, in which the reliability constraints of PG and NGN are formulated based on the multi-scenarios of failure events, and the carbon emission constraints of PG and NGN are introduced by lifecycle carbon emission. A dynamic programming framework based on multi-objective integration is proposed, which can realize rolling planning across time scales to significantly reduce the redundancy of planning results to uncertainty. For multi-objective planning, fuzzy optimization method is used to determine the optimal solution, and the trade-off among economy, reliability and low carbon is achieved. The case study verifies the validity and practicality of the proposed model, and the results show that the proposed multi-objective integrated dynamic programming scheme can improve social welfare more than the planning scheme that only considers the economy or the multi-objective open-loop planning scheme.