Lithium compounds with good solubility in organic solvents?
Under inert conditions you may try dissolving pure metallic lithium. Lithium forms naphtalenide salt , I don't see why di-isopropyl-naphthalene should be any different. 

Another option would be use of 12-crawn-4, which make a lot of salts lipo-soluble. Presence of TMEDA (tetramethylethilendiamine) should affect solubility of many lithium salts as well, though I would focus on salts like benzoate or perchlorate.