The scaling relations between the black hole (BH) mass and soft lag properties for both active galactic nuclei (AGNs) and BH X-ray binaries (BHXRBs) suggest the same underlying physical mechanism at work in accreting BH systems spanning a broad range of mass. However, the low-mass end of AGNs has never been explored in detail. In this work, we extend the existing scaling relations to lower-mass AGNs, which serve as anchors between the normal-mass AGNs and BHXRBs. For this purpose, we construct a sample of low-mass AGNs ($M_{rm BH}<3times 10^{6} M_{rm odot}$) from the XMM-Newton archive and measure frequency-resolved time delays between the soft (0.3-1 keV) and hard (1-4 keV) X-ray emissions. We report that the soft band lags behind the hard band emission at high frequencies $sim[1.3-2.6]times 10^{-3}$ Hz, which is interpreted as a sign of reverberation from the inner accretion disc in response to the direct coronal emission. At low frequencies ($sim[3-8]times 10^{-4}$ Hz), the hard band lags behind the soft band variations, which we explain in the context of the inward propagation of luminosity fluctuations through the corona. Assuming a lamppost geometry for the corona, we find that the X-ray source of the sample extends at an average height and radius of $sim 10r_{rm g}$ and $sim 6r_{rm g}$, respectively. Our results confirm that the scaling relations between the BH mass and soft lag amplitude/frequency derived for higher-mass AGNs can safely extrapolate to lower-mass AGNs, and the accretion process is indeed independent of the BH mass.
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