Which order is "lexicographic order"? To choose 3 items out of 5 items [1, 2, 3, 4, 5], Donald Knuth's lexicographic algorithm (The Art of Computer Programming, Vol 4A, 2011, p. 358, Algorithm L (lexicographic combinations)) gives:

[[1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4], [1, 2, 5], [1, 3, 5], [2, 3, 5], [1, 4, 5], [2, 4, 5], [3, 4, 5]]


or, if strictly following the algorithm, each combination is reversed, making it:

[[3, 2, 1], [4, 2, 1], [4, 3, 1], [4, 3, 2], [5, 2, 1], [5, 3, 1], [5, 3, 2], [5, 4, 1], [5, 4, 2], [5, 4, 3]]


while Combinatorial Algorithms by Nijenhuis and Wilf, 2nd Ed, 1978, p. 26 cited "alphabetic order" or "lexicographic order" of:

[[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 3, 4], [1, 3, 5], [1, 4, 5], [2, 3, 4], ...


so they are different.  Which is actually lexicographic order, or are all of them lexicographic order, and why?
There is no one universally accepted lexographical ordering. Any author is free to introduce their own ordering, as long as it is consistent within their scope of discussion.

It's just like binary tree traversing algorithms like preoder, inorder or postorder traversal. There is no one correct traversal, its upto the author to decide which one to use, and stick with it throughout their discussion about the topic.