I was referring to the "on layout exit" action, but looking at your capx that's not the problem.
Still not sure what you mean by animations, unless that's what you mean by "games". Anyway, that's not an issue either.
Taking a look through your project, I'm pretty sure that the only issue is the size of your images - in terms of disk space. They're too big. 5MB for a simple project like this is huge. The images are simply taking too long to load (as it's their first time doing so when entering the layout) when changing layouts, which causes the delay. It's nothing in your code, you just need to optimise the images in an external image editing program like Photoshop or even GIMP.
I'm testing by compiling this project and even that is taking waaay longer than it should. My PC is churning away to make those sprite strips.
Your other option (which doesn't actually address the problem, it just side-steps it) is to include all or at least half of your images in your first layout, but just outside of the layout itself so they won't be visible. This forces the browser to load the artwork into memory in stages, instead of all at once. This won't reduce the overall lag, but it'll slice it into less noticeable chunks.
Oh, and you don't need to use both the mouse and touch object for input. Touch has a neat property called "use mouse input" which simulates the use of a mouse, meaning you can use the touch object exclusively but it'll accept both mouse and touch input.