Edward de Bono is the creator of the term - lateral thinking = a creative type of thinking also wrote a books on how to teach kids how to think. This helps problem solving and perspective taking and most important help kids try to see the positive in what we are saying and not just the minuses. This can be done if we don't debate but use parallel learning and thinking. His PMI tool is a good example.
here is a link http://tinyurl.com/9z28mtd scroll down - there is a summary of all his thinking tools from his book for kids
OK so if I'm getting this right, it would be like this. Let's say I want my daughter to start on her homework, but it's only Saturday. She wants to wait until Sunday. So we might think of positives (know how much time it'll take so you don't run out of time on Sunday, have it done ahead of time and not have to worry or rush), and negatives (have to put off doing fun stuff she wants to do right then, it's Saturday and Saturdays are supposed to be fun), and then from that try to think of interesting ideas of how to handle it (like look at homework and figure out how long it's likely to take so you know how much time to budget, but then wait until Sunday to do it.)
I guess we do something similar when we have a disagreement. I might say, "I want you to do your homework today because I'm worried it'll take longer than you think and I don't want you getting stressed out tomorrow. You want to play Minecraft instead of doing homework because it's Saturday and you like doing what you want on Saturdays. How can we both get what we want?" Then I leave it up to her to figure out a solution - which she's actually really good at. So I guess that's similar but not exactly the same. However, we do that a lot.
The PMI tool is more of a tool that helps direct thinking in the direction of ' exploring ' an idea rather than critical yes/no thinking. So kids generally automatically reject an idea , here they ' explore ' with an open mind looking at the positives in parallel with us - they given the first shot..
You have described more of a collaborative problem solving scenario. Pure CPS would leave out the solutions - doing hw , either on saturday or sunday and just focus on her concerns first , then your , define the problem and then brainstorm a solution