Temperature measurements by vertically staring ground-based Rayleigh lidars are often used to detect middle atmospheric gravity waves. In time-height diagrams of temperature perturbations, stationary mountain waves are identifiable by horizontal phase lines. Vertically tilted phase lines, on the other hand, indicate that the wave source or the propagation conditions are transient. Idealized numerical simulations illustrate that and how a wave source moving in the direction of the mean wind entails upward-tilted phase lines. The inclination angle depends on the horizontal wavelength and the wave source’s propagation speed. On this basis, the goal is to identify and characterize transient non-orographic gravity waves (NOGWs), e.g., from propagating upper-level jet/front systems, in virtual and actual Rayleigh lidar measurements. Compositions of selected atmospheric variables from a meteorological forecast or reanalysis are thoughtfully combined to associate NOGWs with processes in the troposphere and stratosphere. For a virtual observation over the Southern Ocean, upward-tilted phase lines indeed dominate the time-height diagram during the passage of an upper-level trough. The example also emphasizes that temporal filtering of temperature measurements is appropriate for NOGWs, especially in the presence of a strong polar night jet that implies large vertical wavelengths. During two selected observational periods of the COmpact Rayleigh Autonomous Lidar (CORAL) in the lee of the southern Andes, upward-tilted phase lines are mainly associated with mountain waves and transient background wind conditions. One nighttime measurement by CORAL coincides with the passage of an upper-level trough, but large-amplitude mountain waves superpose the small-amplitude NOGWs in the middle atmosphere.