Classifying acid-base reaction between aluminium hydride and lithium hydride So I was dealing with a reaction the other day, which is also briefly written in the title:


  $$\ce{AlH3(s) + LiH(aq) -&gt; Li+(aq) + AlH4-(aq)}$$


The strange thing is:


Arrhenius definition cannot explain the reaction, since there is no $\ce{OH-}$ in the reaction formula.
Also Brønsted–Lowry definition cannot explain the reaction, because the stuff which $\ce{LiH}$ gives to $\ce{AlH3}$ is not a proton (hydrogenium, $\ce{H+}$) but a protide (hydride, $\ce{H-}$).
And as far as I know, this is the exact definition of Lewis acid and base written in my chemistry textbook:



  
  Lewis acid: A substance which can receive unshared electron pair
  Lewis base: A substance which can give unshared electron pair
  


leading to a conclusion that the above reaction also cannot be explained through the Lewis definition. Below are my questions:


Is there anything wrong in my thought?
Is that really an acid-base reaction? If it is, what kind of acid-base reaction is it?
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.