The pH of a salt solution depends on the hydrolysis of its constituent ions.

1. $AlCl_3$ and $BeCl_2$ are salts of weak bases ($Al(OH)_3$ and $Be(OH)_2$) and a strong acid (HCl). They undergo cationic hydrolysis to produce $H^+$ ions, making their aqueous solutions acidic (pH < 7).
2. $LiCl$ and $BaCl_2$ are salts of strong bases ($LiOH$ and $Ba(OH)_2$) and a strong acid (HCl). Generally, such salts do not undergo hydrolysis and form neutral solutions (pH = 7). However, the $Li^+$ ion has a very small size and high charge density, giving it a much higher polarizing power than the larger $Ba^{2+}$ ion. Consequently, the extensively hydrated $Li^+$ ion undergoes a very slight degree of hydrolysis, making the $LiCl$ solution slightly less basic (or very slightly acidic) compared to $BaCl_2$. Thus, $BaCl_2$ does not hydrolyze at all, maintaining a neutral solution (pH = 7), which is the highest pH among the given options.