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We have measured the wavelength-dependent lags between the X-ray, ultraviolet, and optical bands in the high-accretion rate (⁠|$L/L_{\rm Edd}\approx 40{{\ \rm per\ cent}}$|⁠) active galactic nucleus (AGN) Mrk 110 during two intensive monitoring campaigns in February and September 2019. After including the 2017 data published by Vincentelli et al. we divided the observations into three intervals with different X-ray luminosities. The first interval has the lowest X-ray luminosity and did not exhibit the U -band excess positive lag, or the X-ray excess negative lag that is seen in most AGNs. However, these excess lags are seen in the two subsequent intervals of higher X-ray luminosity. Although the data are limited, the excess lags appear to scale with X-ray luminosity. Our modelling shows that lags expected from reprocessing of X-rays by the accretion disc vary hardly at all with increasing luminosity. Therefore, as the U -band excess almost certainly arises from Balmer-continuum emission from the broad-line region (BLR), we attribute these lag changes to changes in the contribution from the BLR. The change is easily explained by the usual increase in the inner radius of the BLR with increasing ionizing luminosity. [ABSTRACT FROM AUTHOR]