Imaging data is the principal observable required to use galaxy-scale strong lensing in a multitude of applications in extragalactic astrophysics and cosmology. In this paper, we develop Lensing Exposure Time Calculator (LensingETC; https://github.com/ajshajib/LensingETC) to optimize the efficiency of telescope-time usage when planning multifilter imaging campaigns for galaxy-scale strong lenses. This tool simulates realistic data tailored to specified instrument characteristics and then automatically models them to assess the power of the data in constraining lens model parameters. We demonstrate a use case of this tool by optimizing a two-filter observing strategy (in the IR and ultraviolet-visual (UVIS)) within the limited exposure time per system allowed by a Hubble Space Telescope (HST) Snapshot program. We find that higher resolution is more advantageous to gain constraining power on the lensing observables, when there is a trade-off between signal-to-noise ratio and resolution; for example, between the UVIS and IR filters of the HST. We also find that, whereas a point-spread function (PSF) with sub-Nyquist sampling allows the sample mean for a model parameter to be robustly recovered for both galaxy-galaxy and point-source lensing systems, a sub-Nyquist-sampled PSF introduces a larger scatter than a Nyquist-sampled one in the deviation from the ground truth for point-source lens systems.