Internal Order of Adjustments for RAW development

Lightroom is a non-destructive editor. That means that edits you make by changing sliders do not get applied to the data of the image, but are stored as a kind of 'To Do List' in the catalog. Only if and when needed that list is applied to a copy of the image data, and so a new file is created with the edits applied to it. That's for example when you export a file. The order in which the edits are applied is a fixed order, determined by Adobe. 

You can compare this to making an omelette. Lightroom makes the omelette using the Adobe recipe. Your edits are the list of ingredients and the amount of each ingredient. By choosing ingredients and varying the amounts, you determine the outcome of the recipe. But it does not matter whether you first write down the amount of salt and then the number of eggs, or vice versa. No matter in what order you write down the list, Lightroom will never put the salt in the pan first and then add the eggs...

First thing is that as @dj_paige says, the order you change sliders doesn't matter if the slider positions are the same. Adobe has only told us some generalities about this. First is that the order is dynamically adjusted based on what sliders are actually enabled to optimize the speed of the engine. Second, the typical processing order is basically in the sequence you see in the standard layout with some exceptions. First you get the demosaic including sharpening and noise, then camera profile, then whitebalance and exposure and contrast followed by shadows, highlights, etc. including texture etc. Curves come almost last followed only by the special effects such as vignette. 

There is no point whatsoever optimizing how you move the sliders with this in mind by the way. It won't give you better results. The engine optimizes around however you move the sliders and you really can't create any posterization or blow out by doing the slider movements the 'wrong' way around.

I am interested in the order of adjustments that are made to an image if I adjust the sliders. 

Adobe has never told us what that is. And it shouldn't matter, moving slider 1 followed by moving slider 2 should produce the exact same image as moving slider 2 first followed by slider 1.