Classifying acid-base reaction between aluminium hydride and lithium hydride
This is indeed a Lewis acid-base reaction.

The hydride ion has a lone pair which is, in general, not bound to anything. The aluminium atom has at least one unpopulated orbital (typically taken to be a $\mathrm p_z$ orbital in a planar $\ce{AlX3}$ environment). This makes hydride a Lewis base and aluminium a Lewis acid. The association of hydride to aluminium is thus a Lewis acid-base reaction.