On-chip optical filters are a fundamental building block in many optical signal processing applications. Integrated optical filters that can simultaneously achieve narrow bandwidth, low loss, and high extinction ratios are greatly needed. Rare-earth ion-doped crystals have been demonstrated as successful ultra-narrowband optical filters via spectral hole burning. However, such optical filters have only been achieved in bulk crystals, which require high burning powers and are not scalable. In this work, we demonstrate narrowband cavity-enhanced spectral filters based on rare-earth ion-doped thin-film lithium niobate. Specifically, we incorporate thulium ions into high-quality factor ring resonators patterned in thin-film lithium niobate. This approach allows us to achieve different cavity-enhanced filters by controlling the coupling rate of the resonator and burning transient spectral holes in the ring resonance modes. For example, by hole burning in a critically-coupled resonance mode, we demonstrate a narrow bandpass filter (24 MHz) with a high extinction ratio (110) that is 70-times higher than a waveguide of the same length as the ring. Besides the enhanced bandpass filter, we can also create a narrow bandstop filter by using a resonance mode in an initially under-coupled condition. Notably, the bandstop filter changes from Lorenzian- to Fano-shaped due to dispersion when detuned from the cavity, which can be well-modeled by the Kramers-Kronig relations. Such narrowband, high extinction ratio integrated spectral filters could serve as fundamental components for optical signal processing and quantum memories on-a-chip.