When an aqueous solution of lithium chloride is electrolysed using graphite electrodes;

When aqueous solution of NaCl is electrolysed , the following reactions takes place 

${\mathrm{LiCl}}_{\left(\mathrm{aq}\right)}\to {\mathrm{Li}}^{+}+\hspace{0.17em}{\mathrm{Cl}}^{-}+{\mathrm{H}}^{+}+\hspace{0.17em}{\mathrm{OH}}^{-}$

At cathode H⁺ is discharged and at anode Cl^-is discharged. 

Cathode : $2{\mathrm{H}}^{+}+ 2{\mathrm{e}}^{-}\to {\mathrm{H}}_2$

Anode: $2{\mathrm{Cl}}^{-}\to {\mathrm{Cl}}_2+\hspace{0.17em}2{\mathrm{e}}^{-}$

The remaining ions Li⁺ and OH^- ions combine to form LiOH , Hence the pH of the resulting solution increases.