A cloud‐resolved storm and chemistry simulation of a severe convective system in Oklahoma constrained by anvil aircraft observations of NOx was used to estimate the mean production of NOx per flash in this storm. An upward ice flux scheme was used to parameterize flash rates in the model. Model lightning was also constrained by observed lightning flash types and the altitude distribution of flash channel segments. The best estimate of mean NOx production by lightning in this storm was 80–110 mol per flash, which is smaller than many other literature estimates. This result is likely due to the storm having been a high flash rate event in which flash extents were relatively small. Over the evolution of this storm a moderate negative correlation was found between the total flash rate and flash extent and energy per flash. A longer‐term simulation at 36‐km horizontal resolution with parameterized convection was used to simulate the downwind transport and chemistry of the anvil outflow from the same storm. Convective transport of low‐ozone air from the boundary layer decreased ozone in the anvil outflow by up to 20–40 ppbv compared with the initial conditions, which contained stratospheric influence. Photochemical ozone production in the lightning‐NOx enhanced convective plume proceeded at a rate of 10–11 ppbv per day in the 9–11 km outflow layer over the 24‐hr period of downwind transport to the Southern Appalachians. Photochemical production plays a large role in the restoration of upper tropospheric ozone following deep convection. Plain Language Summary Nitrogen oxides are important precursors for tropospheric ozone, an important greenhouse gas. The global amount of nitrogen oxides produced by lightning remains highly uncertain, primarily because of uncertainty in the amount produced per flash. In this paper we use an approach that involves cloud‐resolved modeling with chemistry, constrained by observed flash rates and aircraft measurements of nitrogen oxides, to make an estimate of the mean production per flash for an observed severe storm over Oklahoma. We estimate that the mean production rate was 80–110 mol per flash for this high flash rate storm, which is at the lower end of the range reported in the literature. We use a regional model to follow the outflow of the Oklahoma storm downwind to estimate the amount of ozone produced in the upper tropospheric outflow plume by the lightning‐generated nitrogen oxides. Our estimate is in the range found in previous studies, and we note that the ozone production by photochemistry is an important process in restoring upper tropospheric ozone following storms that lofted low values of ozone from the layer of air near the surface.