There is a method of preparation of LiH by reacting a lithium halide (chloride, bromide, or iodide) with sodium hydride in an inert organic diluent such as tetrahydrofuran. Is it possible to replace a lithium halide with a lithium fluoride?
One problem is the solubility of lithium fluoride. Alkali and alkaline earth fluorides are much less soluble in common solvents than the heavier halides. Lithium fluoride, for instance, is insoluble in alcohol.
Assuming you can get the reaction to go, another problem with fluoride ion in this type of reaction is it has the same charge and similar size versus hydride ion; so you tend to form solid solutions. Such solid solutions are known with various alkali and alkaline earth metal counterions, including lithium. See Ref.  for lithium and Ref.  for calcium.
Such solid solutions may not be a bad thing. The range of compositions they allow can be used to balance hydrogen storage capacity with thermal stability in thermoelectric storage applications. Examples of this application involving various combinations of sodium and magnesium fluorohydrides are given in Refs. [3-5].
Charles E. Messer and John Mellor (1960). "The system lithium hydride-lithium fluoride". J. Phys. Chem. 64, 4, 503–505. https://doi.org/10.1021/j100833a507.
D. Vergnat-grandjean,P. Vergnat,J.-F. Brice,R. Leveque (1979). "Infrared spectra of calcium hydridecfluorude CaF2-xHx", Physica Status Solidi (b) 96, Issue 2 p. 611-616. https://doi.org/10.1002/pssb.2220960215.
T. D. Humphries, D. A. Sheppard, M. R. Rowles, M. V. Sofianos and C. E. Buckley (2016). "Fluoride substitution in sodium hydride for thermal energy storage applications". Journal of Matheuals Chemiatry A 4, 12170-12178. https://doi.org/10.1039/C6TA03623F.
Terry D. Humphries, Jack Yang, Richard A. Mole, Mark Paskevicius, Julianne E. Bird, Matthew R. Rowles Mariana S. Tortoza M. Veronica Sofianos Dehong Yu, and Craig E. Buckley (2020). "Fluorine Substitution in Magnesium Hydride as a Tool for Thermodynamic Control". J. Phys. Chem. C 124, 17, 9109–9117. https://doi.org/10.1021/acs.jpcc.9b11211.
Sheppard, Drew & Corgnale, Claudio & Hardy, Bruce & Motyka, Ted & Zidan, Raigay & Paskevicius, Mark & Buckley, C.E.. (2014). "Hydriding characteristics of NaMgH2F with Preliminary Technical and Cost Evaluation of Magnesium-Based Metal Hydride Materials for Concentrating Solar Power Thermal Storage." RSC Advances 4, 26552 - 26562. https://doi.org/10.1039/c4ra01682c.