Loop Cut will only work with quads, i.e. faces consisting of 4 vertices. When you choose an edge where you want to start the loop cut, it continues over the opposite edge. This means a loop cut cannot be performed if the face has more or less than 4 edges because there is no distinct opposite face.
What you can do in Edit Mode is go into Front Orthographic view by pressing Numpad 1, then K for the Knife Tool, press C for angle constraint > ON and to make sure everything will be cut also press Z for cut through > ON.
Now move the knife to the top edge until a green square appears, left-click, go down to the bottom edge (the angle constraint option provides a straight vertical cut) until another green square appears and left-click again.
To confirm the single cut now press Return. Or instead, to prepare more cuts at once press E, then repeat the left-clicking like before on a different region of the edges. After you've selected all cuts hit Return to confirm.