Referring to the OP diagram, the black wires connected to the top left terminal on the three-way switches are the common hot wires. These receive un-switched power from the line and deliver switched power to the load. The other two terminals are "travelers". Their wires pass live current between the switches. When we add lights to this circuit we don't disturb the travelers. Rather, we insert an additional load between the line and the grounded return.
Specifically, to insert a second light at the second switch we insert it between the hot wire from the line and the common hot terminal of the second switch.
- Hot Common: Black wire from second light is connected to common terminal on second switch (top left in OP diagram). White wire from second light is re-identified as hot (black stripe) and connected to black wire entering second switch box.
- Hot Travellers: Same as OP diagram. Red wire entering second switch box is connected to either lower terminal on second switch (e.g., lower left in OP diagram). White wire entering second switch box is re-identified as hot (black stripe) and connected to other lower terminal on second switch (e.g., lower right in OP diagram).
- Return: Same as OP diagram. White grounded wire entering first switch box is connected to white wire from first light.
- Ground: Green/bare grounding wire from second light is pig-tailed with green/bare grounding wire entering second switch box and a green/bare grounding wire tied to grounding terminal on second switch.