Why do you think you need any 3-wire? Can you show more detail on what are doing with the black/white/red?

the black is hot to switch
the white is neutral
the red is switched

For code compliance you would need to run 3 wire to the switch box as well to provide a neutral there. Or just run the power to the switch first, then 2 wire to the lights.

Oh, I get it now. I didn't get that from your diagram.

If I have to run a 3 wire then how are the 3 wires treated at the switch?

black & red to the switch, white capped for future use with a "Smart" switch.

Thanks for clearing that up joe...you had
me puzzled....appreciated