In inserting the Itemize environment, you jump out of the Lemma environment. Yep, that can be annoying.
To push the Itemize environment (or other) into the above environment (Lemma, in this case), press
Tab while in your itemized list.
To create a shortcut that does this for you in one go, go to
Tools > Preferences > Shortcuts > New and insert as function
command-sequence layout Itemize; command-alternatives completion-accept;cell-forward;tab-insert;depth-increment;outline-in
Assign it a shortcut and you're good to go!
ProTip: I created the function by 1) knowing that one can use the
command-sequence in specifying shortcuts -- it is extremely powerful (example). 2) I knew that you had to use
Tab to push environments -- I'm pretty sure I found that in the LyX documentation. 3) Finally, I looked up what functions
shortcut to insert Itemize executed in the defined shortcuts, and composed the using
I hope this answers your question. In any case, thank you for the "soduko" :)