OK, it goes like this: 14/2 (or 12-gauge, depending on the circuit) from the line to the first switch, which is a 3-way switch. From there, you run 14/3 to the second switch location, which is a 4-way switch. From there, you run 14/3 to the first light location.
From the second light location, run 14/3 to the third switch, which is a 3-way switch. This is a switch loop. I'd use the red and black for the travellers, and mark the white wire black and use that as the switched hot going back to the lights. At the second light, that gets connected to the black of the light fixture.
Now the problem is that, between the two lights, you need four conductors: the two travellers, the switched hot coming back from the third switch, and the neutral. You can get 14/4 romex, but you'll probably have to order it. if the code authority allows, it might be less trouble to run both a 14/3 and a 14/2 between the lights. Make the red and black of the 14/3 be the travellers; use the black of the 14/2 for the switched hot going from the second light to the first light, and connect both whites to the neutral. Be sure you keep those two runs together to the extent possible.
Note that all this assumes that your jurisdiction is not yet requiring that every switch location have a hot and a neutral, for the use of automation devices. If they are, the problem gets more complicated.
From the second light location, run 14/3 to the third switch, which is a 3-way switch. This is a switch loop. I'd use the red and black for the travellers, and mark the white wire black and use that as the switched hot going back to the lights. At the second light, that gets connected to the black of the light fixture.
Now the problem is that, between the two lights, you need four conductors: the two travellers, the switched hot coming back from the third switch, and the neutral. You can get 14/4 romex, but you'll probably have to order it. if the code authority allows, it might be less trouble to run both a 14/3 and a 14/2 between the lights. Make the red and black of the 14/3 be the travellers; use the black of the 14/2 for the switched hot going from the second light to the first light, and connect both whites to the neutral. Be sure you keep those two runs together to the extent possible.
Note that all this assumes that your jurisdiction is not yet requiring that every switch location have a hot and a neutral, for the use of automation devices. If they are, the problem gets more complicated.