New molecular line lists for lithium hydroxide (6Li16O1H and 7Li16O1H isotopologues) covering wavelengths λ > 1 $\mu$m (0-10 000 cm-1 range) are presented. Each line list contains around 300 million transitions between rotation-vibration energy levels with total angular momentum up to J = 95, applicable for temperatures up to T ≈ 3500 K. Line list calculations were based on a previously published, high-level ab initio potential energy surface and a newly computed dipole moment surface of the ground $\tilde{X}\, ^1\Sigma ^+$ electronic state. Lithium-containing molecules are important in a variety of stellar objects and there is potential for LiOH to be observed in the atmospheres of exoplanets. Transit spectra are simulated using the rocky super-Earth 55 Cancri e as an example with two different atmospheric scenarios including LiOH. This work provides the first, comprehensive line lists of LiOH to facilitate its future molecular detection. The OYT7 line lists along with the associated temperature- and pressure-dependent molecular opacities can be downloaded from the ExoMol database at www.exomol.com and the CDS astronomical database.