  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
($M_{\rm BH}<3\times 10^{6} M_{\rm \odot}$) 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.
