I more commonly take one of two approaches: Either I think of a central trick and design a level around that (possibly implementing more tricky stuff along the way), or I simply design a layout then find a solution to work into it. Often this doesn't involve actually
playing and seeing what I come up with; rather, part-way through doing so, I'll get some ideas and from that point on I basically fall back into "design around the trick" mode. I've got a video on my YouTube channel that shows me creating a level - at the start, I have no ideas at all for what the level might look like, but by the end, I've got a complete level (minus a few later backroute fixes). Specifically, "Dangerous Detour" from Lemmings Plus V.
In the case of building around a trick, I do notice that the trick often relates to how crowd control is achieved - you figure out how to control the crowd, and [almost] everything else falls into place - often because the crowd control
also creates part of the route to the exit, or at least part of the route to get another worker where you need them to be. The most notable example of that would be "Drawing Dead" from Lemmings Plus Omega II - I'll do a seperate spoiler tag for the specific details. Don't read it unless you've either solved or given up on that level (or have no interest in playing it in the first place), as this spoiler describes about 80% of the level's solution, including the most important trick.
The crowd is actually contained here by the oldest trick in the book - using blockers to hold the crowd by the entrance. In this case, you only need one blocker, as the other side has a wall anyway. The tricky part is not actually in how to contain the crowd, but how to free them without using up skills you need elsewhere. The level has a Stoner pickup skill, which at first glance may seem useless. The actual way you free the crowd? Use the Stoner on the Blocker, then bash through it. The biggest trick of all is the interaction between crowd control and creating a route - the worker lemming will come back to the start area twice during the solution. I mentioned a wall on one side of the entrance area - above the other side, there is a platform. Quite clearly a worker lemming needs to get to this platform at some point; there's no obvious reason why the crowd would need to (and indeed, they don't need to). The gap between these is VERY slightly more than one builder's length, but one builder is all you have spare to deal with it. The first time the worker gets here though, they need to go back to where they started, so this is perfect - the builder takes them far enough that they fall and walk through the blocker. The stoner is then used on the blocker before they come back again, and that stoner provides the few extra pixels the worker needs to get to the aforementioned platform. When all this falls into place, the rest is very straightforward.
(http://neolemmix.com/levelimg/lpo2/0412.png)
In fact, I notice even when I use the general approach of "just put something together for now, find a solution later", the action often ends up being concentrated near the start of the level for some reason. Probably the most significant example of this is "The Golden Rule Of Lem", one of my NeoLemmix Community Pack submissions - the first half of the level is very action packed, while the second half mostly solves itself once you've got the first half right - but there are plenty of decoy elements in the second half that make you think significant parts of the solution might in fact take place there.
Of course, I do have levels that defy all of these typical elements of my design. "Variety Day" from Lemmings Plus I is an example of this - it could be said to have a core trick (the another-lemming-walks-ahead-of-worker-to-block thingy) but it really is still a puzzle of how everything, overall, fits together.