Expand on this three way switch diagram
First off, that diagram is probably a Code violation

See how they run the travelers in one cable and the switched-hot/neutral in the other cable between the lamps? That can be considered a no-no under NEC 300.3(B)/310.10(H) due to issues with steel boxes and other steel parts (such as a steel stud that both cables run through) getting toasty from inductive heating due to circulating loop currents, as well as excessive 60Hz magnetic fields that can cause EMI.

The fix is simple -- run a single /4 cable (a /2/2 cable can be used instead with one of the neutrals retagged if you can't get /4 in the right size) between the lights, instead of the pair of /2 cables the diagram calls for.

From there, it's easy

Your third box goes between the left and right light boxes, and is wired as follows:


Traveller 1 in the cable from the left light box connects to Traveller 1 in the cable from the right light box, likewise with Traveller 2
All the switched-hots in the box (one from the left box, one from the right box, and one that's the black wire from the fixture) connect together
All the neutrals in the box (again, one from the left box, one from the right box, and one that's the white wire from the fixture) connect together
All the grounds in the box connect together


Tagging wires according to function makes it easier

Tape-tagging wires by function just makes this easier yet.  For instance: tagging all hots black, all switched hots red, and all travelers say yellow for one traveller and blue for the other in this scenario means that you can simply connect like-color-tagged wires together and have everything work.