[see my edit below] No, Arc Fault Circuit protection is not required on lighting circuits. Article 210.12 reads in part:
210.12(A) Dwelling Units. All 120-volt, single-phase, 15- and 20-ampere branch circuits supplying outlets or devices installed in dwelling unit kitchens, family rooms, dining rooms, living rooms, parlors, libraries, dens, bedrooms, sunrooms, recreation rooms, closets, hallways, laundry areas, or similar rooms or areas shall be protected by any of the means described in 210.12(A)(1) through (6):
You are good as long as you are not overloading a circuit and I would be very surprised if adding 3 lights overloads your circuit.
Your plan is good. Carry on.
[Edit] After re-reading that section and the definitions I believe @Paul Logan is correct. Switches are devices and luminaires are fed from lighting outlets. This is probably why my state has elected not to follow 210.12 in single and two family dwelling. The requirements are quite onerous for just about every circuit in the house. Your inspector may enforce this section for lighting and require AFCI protection on this modified circuit.