Somehow this topic reminds me of my work before. There were a lot of "consultant speak" such as lateral thinking, thinking organisations, learning organisations, from the gurus such as edward de bono, dave ulrich, and the guy who moved cheese.
I don't know how much of this can be taught or forced. Example problems illustrating lateral thinking tend to have one "right answer".
I prefer to understand and assimilate processes, identify patterns across industries and data. I don't think I deliberately think laterally. But I just try my best to think in as many ways as I can. Lateral, vertical, diagonal, random, tangent, off-tangent...
Despite my tone that sound like one of the many people who think that these strategies are just fluff, I am someone who fervently believes in systems and processes and metaprocesses, and not just in them, but that they can be learnt.
I like to akin the learning of skill as the installation of an APP in my brain (analogous to the smart phone). And since I enjoy learning, I do enjoy installing new apps in my mind.
I read books on thinking systems all the time. One of my favourites is Peter M Senge's The 5th Discipline.
This is perhaps also related to my educational background being in psychology.