Using 14/3 to wire a fan and lights separately
Yes, that will work. Terminate the 14/3 (neutral and two switched hots) in the ceiling fan box where you'll hook up the neutral and a switched hot to the fan. Then connect the 14/2 for your light to the neutral in the fan box and to the other switch hot. Run the 14/2 to your light locations. You will naturally want to hook up all the ground wires to these fixtures.