The atomic radius of chlorine is smaller than the radius of lithium. The smaller the nucleus/atomic radius of an atom the closer in proximity of electrons to the nucleus of the atom, which generates a greater attraction. Consequently, more energy is required to break the attraction to remove the first electron from chlorine because the first electron is closer to the nucleus compared to lithium. Think of magnets: the closer the magnets are together, the harder it is to pull them apart.
