Spark-ignition (SI) engines emerge as a viable solution for specific marine applications, offering low-noise operation and emissions mitigation, as well as great potential to utilize high-octane number alternative fuels, such as methanol, ammonia, and hydrogen. However, heavy-duty (HD) SI engines still face challenges such as knocking and combustion instability. Particularly for lean combustion conditions, these engines exhibit the most pronounced cyclic combustion variations. This paper investigates the combustion stability of a 500 kW marine lean-burn natural-gas (NG) engine, a promising candidate for reducing emissions in marine applications. We focus on analyzing in-cylinder pressure measurements to quantify combustion characteristics, emphasizing cycle-to-cycle combustion variation, and exploring the influence of operating parameters like spark timing (ST) and air excess ratio (λ). Our findings demonstrate a clear trade-off between NO_x and COV_IMEP emissions through variations in the λ and ST. We identified a transition zone characterized by an increasing number of late-burning cycles at higher λ, before partial burning cycles began at further dilution. Following this, we established a new threshold of 6% for COV_IMEP to determine unstable combustion. Notably, increasing dilution from a λ of 1.12 to 1.61 decreased NO_x emissions from 17.83 g/kWh to 0.16 g/kWh, well below IMO Tier III standards, while COV_IMEP increased from 1.72% to 13.42%. These insights highlight the potential for advancing SI technology for marine applications and the need for further research to optimize both combustion and emissions in such engines.