Step 1: What controls melting point.
Strong ionic lattices melt high, while covalent molecular solids melt low.
Step 2: Spot the covalent one.
The small, highly charged aluminium ion polarises bromide strongly, so AlBr$_3$ is covalent and exists as Al$_2$Br$_6$.
Step 3: Compare.
LiBr, NaBr and MgBr$_2$ are ionic and melt high, so AlBr$_3$ melts the lowest.
Step 4: Answer.
\[ \boxed{\text{AlBr}_3} \]