Why has lithium bromide a slight solubility in organic solvents?
Lithium bromide is a salt of small cation and large anion. They cannot interact effectively, so the crystal lattice is quite easy to break. On the other hand, lithium cation is small, so it can interact effectively with small negatively charged atoms, like oxygen. Indeed, lithium cation has highest hydration energy of all alkaly metal cations. Altogether, it means, that in solvents with oxygen atoms (alcohol, esters, acetone) lithium cation effectively bounds to solvent molecules, leaving crystall lattice, and bromide has to follow, resulting in some solubility of lithium bromide in solvents with negatively charged oxigen and to lesser extent, nitrogen (for example pyridine). Lithium bromide is still insoluble in organic solvents that cannot interact with lithium cation, like benzene.