Electrically speaking, you can't put a 4- way between the first 3-way and the lights. Electrically the 4-way must go between the 2, 3-ways. You can't just use joed's drawing and put a 4- way in anywhere you want to. You can draw it that way, but you still must run the wires from the 4-way to both 3-ways, or make one hell of a mess in the fixture boxes with all the splices that you would need to make, and still you will need 4 conductors and a ground to the 4-way.
Are you doing this job in conduit or using Romex? If you're using Romex you will need to buy 2 wires, 3 wires, 4wires, and 6 wires inbetween different sections, so you will need to run more than one cable between points anyways as you won't be able to find those cables.
Your initial question was "is it possible without doubling back at the 3rd switch?" The answer is still No. You can run wires in many different configurations, but you will not save wires and you will make it much more confusing by trying to hit the lights inbetween the switches, and I don't think you really want to try to figure out all the wires that are going to be in your switch boxes if you don't know how to wire a 4-way in the first place.