Spin–lattice relaxation measurements are used in 7Li NMR studies of materials of potential use in solid-state Li-ion batteries as a probe of ion mobility on a fast (nanosecond to picosecond) time scale. The relaxation behavior is often analyzed by assuming exponential behavior or, equivalently, a single T 1 time constant. However, the spin–lattice relaxation of spin I = 3/2 nuclei, such as 7Li, is in general biexponential; this is a fundamental property of I = 3/2 nuclei and unrelated to any compartmentalization within the solid. Although the possibility of biexponential 7Li (and other I = 3/2 nuclei) spin–lattice relaxation in the solid state has been noted by a number of authors, it can be difficult to observe unambiguously using conventional experimental NMR techniques, such as inversion or saturation recovery. In this work, we show that triple-quantum-filtered NMR experiments, as previously exploited in I = 3/2 NMR of liquids, can be used in favorable circumstances to observe and readily quantify biexponential 7Li spin–lattice relaxation in solids with high ion mobility. We demonstrate a triple-quantum-filtered inversion-recovery experiment on the candidate solid electrolyte material Li2OHCl at 325 K, which has previously been shown to exhibit fast ion mobility, and we also introduce a novel triple-quantum-filtered saturation-recovery experiment. The results of these solid-state NMR experiments are less straightforward than those in liquids as a consequence of the unwanted direct excitation of triple-quantum coherences by the weak (compared with the unaveraged 7Li quadrupolar interaction) pulses used, but we show that this unwanted excitation can be accounted for and, in the example shown here, does not impede the extraction of the two 7Li spin–lattice relaxation times.