Programmable cavity-enhanced telecom quantum memory in thin-film lithium niobate

Spectrally multiplexed telecom quantum networks require quantum memories combining efficient storage with programmable frequency addressing. An integrated implementation should therefore unite a native telecom transition, efficient storage, and fast on-chip spectral control. Here we demonstrate a cavity-enhanced memory in an isotopically purified $^{167}\mathrm{Er}^{3+}$-doped thin-film lithium niobate microring. Long-lived hyperfine shelving states enable persistent, high-contrast atomic frequency comb preparation with a single-component lifetime of $277.6(52.6)$~s, while cavity impedance matching yields $23.3(5)\%$ on-chip efficiency for 100-ns storage. The intrinsic electro-optic response enables frequency-selective storage and routing at rates up to 20~MHz. We further store and retrieve time-energy-entangled telecom photons, violating an entanglement-witness bound by more than 11 standard deviations. Our results establish erbium-doped thin-film lithium niobate as a programmable light--matter interface for spectrally multiplexed quantum networks.