Can a Lewis structure be drawn for any bonded molecule?
Usually, but the formalism is generally applied to bog standard 2 centre, 2 electron bonds.
Even for carbon chemistry, we have difficulty accurately representing the skeletal formula of benzene. English A levels have prescribed a hexagon and an enscribed circle; at undergraduate level 1,3,5-cyclohexatriene would be represented. These representations are of course formalisms, by which I mean a prescribed or traditional form within the discipline (do I really mean that? I stole that definition off a dictionary site, let me try again).
Carbon chemistry traditionally represents molecules as catenated