If a chlorine atom were to attract an extra electron from lithium, the lithium atom would become positively charged.
A Lithium atom has two electrons orbiting in the inner shell and only one electron orbiting in its outermost shell. The outer shell is incomplete and therefore unstable.
Lithium atoms readily give up one electron to form a positively charged Lithium ion. In so doing , it obtains the same stable configurations as the noble gas helium.
All group one atoms can lose one electron to form positively charged ions.