Those numbers are really weird, I'm thinking they may be inaccurate or taking too many things into account and not taking others. Damage to towers and creeps is all physical, but that physical damage dealt seems REALLY high. To be honest, the end-game damage stats are almost never worth looking at. The main important things are gold, creep kills, items, score.
In general your build is fine, though ninja tabi was a bad choice unless the other team was almost entirely AD, in which case it was at least arguable but not optimal. Lux is a long-range character, and if you're at the range where you need Ninja Tabi's armor, you're probably too close to the fight. Sorc Shoes or Ionian Boots are usually better on her, you had no CDR on Lux who works well with CDR. However, all items you bought gave AP in some way, which is fine and what you should be doing. But like I said, try to squeeze some CDR in there, usually in the form of Ionian Boots.
It seems like the endgame damage numbers are just weird, don't pay any attention to them and keep doing what you're doing.
EDIT: Even veterans can learn something new. Turns out Lichbane does in fact do physical damage, I had always assumed that since it's based off your AP that it did magic damage. Interesting. Well that certainly explains it. Makes the numbers look really weird, eh?
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