A base anhydride is an oxide of a chemical element from group 1 or 2 (the alkali metals and alkaline earth metals, respectively).
They are obtained by removing water from the corresponding hydroxide base.
If water is added to a base anhydride, a corresponding hydroxide salt can be [re]-formed.
However, they are Lewis bases, because they will share an electron pair with some Lewis acids, most notably acidic oxides.
[1] They are potent alkalis and will produce alkali burns on skin, because their affinity for water (that is, their affinity for being slaked) makes them react with body water.