Unit cell structure of ionic crystal
I looked and there are a lot of questions on the site about units cells, many of which are pertinent. However I couldn't find one that answers your question directly. 

First there is no reason to guess that $\ce{LiH}$ has a FCC structuree. You can look that up, for instance in Wikipedia. 

Second $\ce{LiH}$ doesn't really have molecules in the solid. Think of $\ce{LiH}$ as  an empirical formula rather than a molecular formula. 



UNIT CRYSTAL

I lifted the following from website https://opentextbc.ca/chemistry/chapter/10-6-lattice-structures-in-crystalline-solids/



Now the text says:


  The unit cell contains four sodium ions and four chloride ions, giving the 1:1 stoichiometry required by the formula NaCl. 


That is correct. The unit cell must have the correct stoichiometric ratio. However the section seems to imply that the middle drawing, as show below, is the proper unit cell. It isn't!



First realize that when looking at proper unit cells is that that the lattice points between which the edges are drawn are the nuclei, not points in space that would contain whole atoms. So consider the drawing below. For the cell as shown in the illustration, there are 8 corners with 1/8 atom each. Four corners are Na, and four are Cl. Thus the cell shown only has $\frac{1}{2}$ of a Na cation and $\frac{1}{2}$ of a Cl anion. 



Now down the rabbit hole!

The proper unit cell for NaCl is shown below:



From Wikipedia article on Cubic crystal system:


  The face-centered cubic system (cF) has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of 4 lattice points per unit cell (​1⁄8 × 8 from the corners plus ​1⁄2 × 6 from the faces). Each sphere in a cF lattice has coordination number 12. Coordination number is the number of nearest neighbors of a central atom in the structure.


So the unit cell contains $\ce{Na4Cl4}$ !?!

The reason is that the proper unit cell must also contain all the symmetry elements of the crystal. Look at the drawing below:



I won't get into all of how group theory applies to crystals and molecules, but the  red line shows a four-fold rotation axis. In other words all the atoms are identical. You can rotate the crystal 90 degrees about the red axis and the sodium and chlorine atoms are in identical spots. The axis is a four-fold axis because you have to rotate 90 degrees four times to get the identical atoms back to their starting position.