Two switches on the same single hot wire
This is called a switch leg the white should be taped black or another hot conductor color.
Your red and black are the switched hots going to the lights.
You don’t have a neutral in your case so your dimmer can not require a neutral it is possible a dimmer that requires a ground will work if the ground is connected at the other end and back at the panel but most LED’s won’t work with an old school dimmer because they draw a little current through the light this causes LED’s to glow or flash but will be fine with incandescent lamps on a dimmer. That’s why I mentioned the possibility of a dimmer that uses the ground may be an option for LED’s.