Question

lithium + gold(III) chloride +lithium chloride + gold

need to balance equation

Answer 1

You can't balance this. You have no arrow. There is no separation of products and reactants. If yu intended the arrow to go here.
3Li + AuCl3 ==> 3LiCl + Au

Answer 2

Lithium(s)+gold(iii)chloride(aq)+ gold(s)