Is lithium lipid soluble in the body?

I am working of a drug project. I am jsut confused because I umed that if a drug is lipid soluble then it is probably primarily excreted through bile and not the kidney. Well, my drug (that I made up for pharmacology cl) is lipid soluble because it has to cross the Blood brain barrier in order to exert it's effects on the brain...and lithium enter milk so I ume it is lipid soluble but my drug book says it is excreted unchanged through the kidneys...? how do you explain a lipid soluble drug being excreted unchanged through the kidneys? Thanks alot.