Solubility of metal halides
$\ce{LiCl}$ and $\ce{LiBr}$ are ionic compounds with a significant covalent character. This is due to the strong polarising power of $\ce{Li^{+}}$ cation. This polarising power is due to its large charge to mass ratio.

$\ce{Li^{+}}$ pulls the electron cloud of the halogen, hence resulting in a covalent character. The covalent character is more in $\ce{LiBr}$ than $\ce{LiCl}$ as $\ce{Br^-}$ is larger in size, hence valence shell is held comparatively loosely.


This is what essentially happens.