The dissociative recombination of LiH+ ions with low-energy electrons is observed at a storage ring and the final states are analyzed using fragment imaging and field ionization techniques. The rate coefficient is found to be larger than its estimated value used in astrophysical models. Mostly the highest energetically possible Rydberg states of the lithium atom are populated by the reaction, indicating a common trend for molecular recombination via the noncrossing mode.