I have a surplus of 14/2 and a little bit of 14/3, and this project is price-sensitive, so I drew up this plan to make use of what I have on hand. It minimizes the length of 14/3 needed because that's all I have on hand. All switches and lights have neutrals and grounds accounted for - I just want to make sure I'm allowed to use a 14/2 cable as two travelers without a neutral.
This is not allowed because it violates the rule that in any cable there must be two conductors carrying equal current in opposite directions so the magnetic fields cancel. That T- T Loop top right would have one traveler carrying current, no current in the other, and no neutral present carrying current in the opposite direction.
The time varying magnetic field around the cable could induce currents in nearby conductors and cause heating.
Since you are going to have to buy more cable, consider getting 14/4 + gnd and connecting the two switches in the arrangement called three-wire control. This gives a neutral and a constant line hot in both switch boxes. I recently came across an article¹ for a UK audience touting three wire control as superior to the traditional two wire control for connecting a pair of 3-way switches. I don't know if this is being done in the US.
The presence of both a line hot and a neutral in all switch boxes may be useful in the future, and the immediate benefit would be that you could easily extend the circuit to put a receptacle in the wall below. Such a receptacle would be independent of the two 3-way switches.
For the record, smart switches
In this case use smart switches that use wireless or powerline signaling, such as Insteon. The smart switch master goes at the left switch and the AC powered (but wireless communicating) remote goes on the right switch.
In this case the 14-2 between lamps has its black wire re-marked red using tape.
The 14-2 from the right lamp to the right switch is deleted altogether.
Now red = switched-hot, black = always-hot, white=neutral and Bob's your uncle.