One battery energy storage system (BESS) can be used to provide different services, such as energy arbitrage (EA) and frequency regulation (FR) support, etc.， which have different revenues and lead to different battery degradation profiles. This paper proposes a whole-lifetime coordinated service strategy to maximize the total operation profit of BESS. A multi-stage battery aging model is developed to characterize the battery aging rates during the whole lifetime. Considering the uncertainty of electricity price in EA service and frequency deviation in FR service, the whole problem is formulated as a two-stage stochastic programming problem. At the first stage, the optimal service switching scheme between the EA and FR services are formulated to maximize the expected value of the whole-lifetime operation profit. At the second stage, the output power of BESS in EA service is optimized according to the electricity price in the hourly timescale, whereas the output power of BESS in FR service is directly determined according to the frequency deviation in the second timescale. The above optimization problem is then converted as a deterministic mixed-integer nonlinear programming (MINLP) model with bilinear items. McCormick envelopes and a bound tightening algorithm are used to solve it. Numerical simulation is carried out to validate the effectiveness and advantages of the proposed strategy.