At 120v these lights will draw exactly 4.0 amps. On a 15 amp lighting circuit, you are not allowed to exceed 12 amps, which is the 80% of circuit capacity max allowed by NEC for lighting and other continuous load items. You will be right at the limit, do NOT connect anything else to the circuit.
If you are running #12 wire, I'm not sure why you want to use a 15 amp breaker, you should be using a 20 amp breaker.
The "branch circuit" you are describing is technically known as a
multi-wire circuit and sometimes also known as an Edison multi-wire circuit. There is no need or requirement to upsize the shared neutral on a multi-wire circuit.
You may wish to read up on multi-wire circuits before you start, it will take a fair amount of planning, and for best efficiency you will want a balanced circuit, having an equal number of lights on each side of the circuit, this reduces the load on the neutral to zero in places and in others, it is only the load of one or two lights, depending on how you wire it up.
I used three separate MW circuits each powering four lights, with double pole switches controlling each circuit.
Forgot, you've already seen my thread..........
Charles