Lateral thinking may be dreams or even nightmares. It is a form of supine thought which could be induced by a deep sleep or often enough (insomnia) if one choses to stay in bed whilst ruminating.
Vertical thinking, a sapient state, synonymous with **** Erectus, can be accurately described as “ Pensée Avec La Petite Tete “ which is more of a male domain, usually accompanied by R.E.M.