  We present the tidal disruption event (TDE) AT2022lri, hosted in a nearby
($\approx\!144$ Mpc) quiescent galaxy with a low-mass massive black hole
($10^4\,M_\odot < M_{\rm BH} < 10^6\,M_\odot$). AT2022lri belongs to the
TDE-H+He subtype. More than 1 Ms of X-ray data were collected with NICER,
Swift, and XMM-Newton from 187 d to 672 d after peak. The X-ray luminosity
gradually declined from $1.5\times 10^{44}\,{\rm erg\,s^{-1}}$ to $1.5\times
10^{43}\,{\rm erg\,s^{-1}}$ and remains much above the UV and optical
luminosity, consistent with a super-Eddington accretion flow viewed face-on.
Sporadic strong X-ray dips atop a long-term decline are observed, with
variability timescale of $\approx\!0.5$ hr--1 d and amplitude of
$\approx\!2$--8. When fitted with simple continuum models, the X-ray spectrum
is dominated by a thermal disk component with inner temperature going from
$\sim\! 146$ eV to $\sim\! 86$ eV. However, there are residual features that
peak around 1 keV, which, in some cases, cannot be reproduced by a single broad
emission line. We analyzed a subset of time-resolved spectra with two
physically motivated models describing either a scenario where ionized
absorbers contribute extra absorption and emission lines or where disk
reflection plays an important role. Both models provide good and statistically
comparable fits, show that the X-ray dips are correlated with drops in the
inner disk temperature, and require the existence of sub-relativistic
(0.1--0.3$c$) ionized outflows. We propose that the disk temperature
fluctuation stems from episodic drops of the mass accretion rate triggered by
magnetic instabilities or/and wobbling of the inner accretion disk along the
black hole's spin axis.
