We present the tidal disruption event (TDE) AT2022lri, hosted in a nearby (≈144 Mpc) quiescent galaxy with a low-mass massive black hole (104M⊙ < MBH < 106M⊙). 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 to 672 days after peak. The X-ray luminosity gradually declined from 1.5 × 1044 erg s−1 to 1.5 × 1043 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 a variability timescale of ≈0.5 hr–1 days and amplitude of ≈2–8. When fitted with simple continuum models, the X-ray spectrum is dominated by a thermal disk component with inner temperature going from ∼146 to ∼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 a scenario either 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 subrelativistic (0.1–0.3c) 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.