Is there a notion of generalized acidity for lithium ions?
A complex of lithium ion with lithium hudroxide is known as the salt $\ce{[Li2OH]^+[ClO4]^-}$ [1].  As with the hydronium salt, this requires an essentially nonbasic counterion; with a chloride counterion a double salt is obtained with no evidence of a complex cation.  From the abstract (some evident faults in translation from Russian have been corrected):

An effort is made to obtain salts of Li2OH+ and Li3O+ cations, belonging to a series of simple oxonium compound cations H3O+, LiOH2+, Li2OH+, Li3O+, where proton and lithium replace each other. Binary compounds of lithium hydroxide with lithium chloride and perchlorate are obtained: LiOH·LiClO4, LiOD·LiClO4, LiOH·LiCl, LiOD·LiCl and LiClO4·2LiOH. A conclusion is made by IR absorption spectra, that an adduct with perchlorate can be built of ClO4 anions and complex [Li2OH]+ cations. For adducts with chloride, equivalence of hydroxide and chloride anions with regular alternation of the anions in the crystal lattice is most probable.

Reference
1.
Nikitina, Z. K., Nikitina, N. I., Rosolovskii, V. Y., &quot;Complexing Lithium Salts and Lithium Oxide or Hydroxide: Synthesis and Characterization of a New Cation-Lithiumhydroxonium Li~2OH^+&quot;, Russian Journal of Inorganic Chemistry 42(9), 1295-1298  (1997).