  Long-lived sub-levels of the electronic ground-state manifold of rare-earth
ions in crystals can be used as atomic population reservoirs for photon
echo-based quantum memories. We measure the dynamics of the Zeeman sub-levels
of erbium ions that are doped into a lithium niobate waveguide, finding
population lifetimes at cryogenic temperatures as long as seconds. Then, using
these levels, we prepare and characterize atomic frequency combs, which can
serve as a memory for quantum light at 1532 nm wavelength. The results allow
predicting a 0.1\% memory efficiency, mainly limited by unwanted background
absorption that we conjecture to be caused by the coupling between two-level
systems (TLS) and erbium spins. Hence, while it should be possible to create an
AFC-based quantum memory in Er$^{3+}$:Ti$^{3+}$:LiNbO$_3$, improved crystal
growth together with optimized AFC preparation will be required to make it
suitable for applications in quantum communication.
