The flight control responses of the fruitfly represent a powerful model system to explore neuromotor control mechanisms, whose system level control properties can be suitably characterized with a frequency response analysis. We characterized the lift response dynamics of tethered flying Drosophila in presence of vertically oscillating visual patterns, whose oscillation frequency we varied between 0.1 and 13 Hz. We justified these measurements by showing that the amplitude gain and phase response is invariant to the pattern oscillation amplitude and spatial frequency within a broad dynamic range. We also showed that lift responses are largely linear and time invariant (LTI), a necessary condition for a meaningful analysis of frequency responses and a remarkable characteristic given its nonlinear constituents. The flies responded to increasing oscillation frequencies with a roughly linear decrease in response gain, which dropped to background noise levels at about 6 Hz. The phase lag decreased linearly, consistent with a constant reaction delay of 75 ms. Next, we estimated the free-flight response of the fly to generate a Bode diagram of the lift response. The limitation of lift control to frequencies below 6 Hz is explained with inertial body damping, which becomes dominant at higher frequencies. Our work provides the detailed background and techniques that allow optomotor lift responses of Drosophila to be measured with comparatively simple, affordable and commercially available techniques. The identification of an LTI, pattern velocity dependent, lift control strategy is relevant to the underlying motion computation mechanisms and serves a broader understanding of insects' flight control strategies. The relevance and potential pitfalls of applying system identification techniques in tethered preparations is discussed.