I want to make a shortcut at LyX that if I press it I'll get what the
\displaystyle does (in math mode).
e.g.: If I'll press Ctrl+I I'll get an integral...
Is there a way to do this?
You can at least make a shortcut to insert just
\displaystyle, if that is OK. Go to Tools --> Preferences --> Editing --> Shortcuts (see Shortcuts for Lemma, Claim, Theorem etc for a screenshot). Click New, and in the Function field write
Enter whichever shortcut you would like. If the shortcut already exists, LyX will inform you of this, and you have to either choose a new shortcut, or edit the existing command.