AGN STORM 2. XII. Ground-based Optical Photometry and Lag Measurements of Mrk 817

We present the ground-based imaging campaign and light curves of Markarian 817 as part of the multiwavelength monitoring program AGN STORM 2. Observations were carried out over 1.4 yr in the uBgVriz filters, with a median cadence of 0.4 day in the g band. Reverberation lags are measured using three methods (interpolated cross-correlation function (ICCF), Just Another Vehicle for Estimating Lags In Nuclei, and PyROA) with the Swift UVW2 band (1928 & Aring;) as the reference light curve. The ICCF centroid lags range from 3.0 +/- 0.8 days for the u band up to 7.9 +/- 1.5 days for z, and are consistent with a tau proportional to lambda 4/3 dependence, the relation expected for lamppost reprocessing by a Shakura-Sunyaev disk. Lags measured with the other methods are systematically shorter, and deviate from a lambda 4/3 power-law spectrum at long wavelengths. The lags exceed thin-disk reprocessing predictions by factors of similar to 3-6, similar to the "disk size discrepancy" seen in other Seyfert galaxies. We divide the campaign into three epochs with different levels of mean luminosity and X-ray obscuring column density and find that the lags vary by as much as a factor of 2 between epochs. The intrinsic spectral energy distribution is bluer and brighter during the first third of the campaign, and the longest continuum reverberation lags are obtained during that period. These results suggest that changes in ionizing luminosity can produce large variations in continuum lags on short timescales by altering the diffuse continuum luminosity emitted by the broad-line region (BLR) and/or obscuring outflow, although changes in obscuration between the central engine and BLR may also contribute to the lag variations.