As described in the comments, there really is no sharp boundary between "ionic" and "covalent" bonding. With metal hydrides the situation is muddled further because the usual electronegativity-difference rules don't really work. Not only lithium but also magnesium forms a hydride whose ionic character far exceeds what would seem to be expected from electronegativity differential.
Magnesium hydride, sometimes called "covalent" or "borderline covalent" (I've even seen "polymeric") with its electronegativity difference less than unity, nonetheless has a crystal structure (rutile) generally associated with compounds having a higher degree of ionic character; the magnesium is octahedrally coordinated just as in the oxide or fluoride (the latter also has a rutile structure). Moreover, it serves readily as a hydride-ion source to water, if the passivating hydroxide layer is broken by either physical milling or chemical doping .
Lithium hydride shows similarly high ionic character even though here too the electronegativity differential would seem too small. It has a rock-salt structure like the fluoride or chloride, and reaction with water is again limited by saturation of the solution  (a more forgiving limit than with magnesium hydroxide) rather than lack of hydride-ion availability.
What happens in terms of atomic structure is the hydrogen 1s valence orbital is simply too small to offer good covalent overlap with the relatively diffuse valence orbitals offered by most alkali and alkaline-earth metals. The orbitals of lithium among alkali metals and magnesium among alkaline-earth metals are just a little too diffuse to optimize covalent bonding to hydrogen, and so the hydrides tend more to ionic bonding than would otherwise be the case (beryllium, with a smaller cation radius, does offer better overlap and its hydride does show more covalency). Heavier metals in both groups serve only to make the overlap situation worse and the bonding forced even more towards ionic.
The role played by the relatively small size of the hydrogen is consistent with Fajan's Rules after all, as these rules favor ionic bonding with small anions. Hydride ion is very much "puffed-up" compared with the parent atom but still is comparable in size with fluoride ion.
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J. H. Leckey, L. E. Nulf, and J. R. Kirkpatrick. "Reaction of Lithium Hydride with Water", Langmuir 1996, 12, 26, 6361–6367. https://doi.org/10.1021/la950843h.