I think there may be a slight misunderstanding.
I think you are thinking of ionic compounds in electrolysis, which have to be molten (or aqueous, if possible) for it to work. That is because in a solid ionic lattice, the ions are not free to move and conduct the electric current. When ionic compounds are molten, or aqueous, the ions are free to move and carry a current.
Metals are conductive, no matter whether they are molten or not, due to delocalised electrons. You don’t electrolyse a metal, because it’s already a pure substance and you don’t need to separate it into anything.