I could follow up until that last paragraph Theorist. Just because we don't know the decryption code that translates electromagnetic impulses in our brain into coherent data (not talking EEG, I mean thoughts directly to a computer), it doesn't mean that memories or feelings or any other sensation we perceive are something more than electrical impulses caused by chemical reactions.

As for the differences between the lucid self and the waking self, Ill give a simple example. Think of your brain as a road map, now when you want to get from one destination to another, you follow the roads to get from 'A' to point 'B'. But when you are lucid you can forget the roads (preformed neural networks from waking life) and just draw a straight line from 'A' to 'B' or zig zag all over the place if you don't have good dream control. The differences in mental state (therefore actions and behaviors) come from the "unnatural" mental state of lucid dreaming, which in an MRI looks like a composition of a waking person's and a non-lucid dreaming person's scans.

And you are right, there is no such thing as a constant self, each experience you have affects you in some way, so of course it will change you, but most of the time the effects are negligible, and the only things that cause any measurable change are major or repeated events.