Is there any specific way in LyX of binding a key to the following operation:
a) go into math mode b) copy the immediately preceding piece of math, eg the last equation
at the current point of the cursor?
In LyX you can use
ctrl+m sequence or
shift+ctrl+m sequence in order to enter into inline math-mode or display math-mode, respectively. Then you can use
ctrl+a to select the whole equation inside your math environment.