Ring opening, nucleophilic substitution
The free electron pairs of the oxirane may act as a Lewis base and coordinate with a Lewis acid like $\ce{Li+}$.  This form of activation facilitates the attack of the alanate $\ce{[AlH4]-}$ as a $\sigma$-nucleophile at the less substituted side of the epoxide.

Once opened, the nucleophilic oxygen attacks at the electron deficient centre of $\ce{AlH3}$ (Lewis acid).  But the $\ce{Al-O}$ bond hydrolyzes upon the workup, yielding the alcohol and the hydroxides of lithium and aluminum.