For the detailed understanding of transient combustion processes, in particular, of auto-ignition, quantitative measurements with high spatio-temporal resolution are desirable. These can, for instance, serve as validation data for time-resolved numerical simulations and in particular for the combustion models used in those simulations. In the current study, a jet-in-hot-coflow (JHC) burner, developed at the German Aerospace Center (DLR), the DLR JHC, was used to inject a turbulent methane jet into the hot exhaust gas of a lean hydrogen/air flame, and a steady state jet flame was established. In addition, fuel could be injected in a transient manner. Here, an auto-igniting jet was observed. The flame stabilization of the steady state jet flame and the auto-ignition during transient fuel injection were studied using high-speed laser-based and optical measurements. A strategy for quantifying high-speed OH planar laser-induced fluorescence is presented, and the measurement uncertainties are evaluated. The flame stabilization mechanism in steady state jet flames was assessed using probability density functions of the OH concentration at different axial and radial locations. The formation of auto-ignition kernels during transient fuel injection is evaluated based on time series of the OH concentration. It is shown how the OH concentration levels and PDF shapes can be used to characterize the chemical state of the reacting flow and to distinguish between auto-ignition and flame propagation.