Will this 3 way switch wiring plan work?
Don't waste your time.  Have a /3 cable bypass the lamps.
This is a rather straightforward problem if you aren't trying to snake the travelers through the bulb sockets.  I know you imagine some great cost savings in wire by doing that... forget it.
Besides... running travelers through the bulb sockets is pointless, and takes up a LOT of splice space inside the box.  The common octagon box doesn't have the cubic inches to spare for those splices.  (you need 2.25 cubic inches per wire entering the box, so passing the travelers through just wastes 9 cubic inches, leaving precious few for the task at hand.
Unless you want to do this with smart switches. Then your &quot;/3 for everything&quot; plan is fine.
The drawings above don't work anyway
The upper drawing, I can't believe it was drawn out in &quot;pro grade&quot; quality, since it's utterly incompetent.  (Here's a paid JustAnswer this was told to a customer; comedy follows.)  With the left switch down, all bulbs are dead (no power enters the system). With the left switch up, your choices are either L2 lit, or both wired in series. &quot;What were they thinking?&quot;
The lower drawing is a is a hillbilly hack to avoid paying for the proper /4 cable, and violates NEC 300.3.
Again, no reason on earth to drag travelers through octagon boxes.  Just have a /3 cable fly from switch to switch, bypassing the lamps.  Then make the lamp string a &quot;spur&quot; off ONE of the switch boxes, all with /2.  And you're done.
Or use smart switches. You need /3 between the smart switch master and all lamps.  (black=always-hot, red=switched-hot, white=neutral).