Is this proof for showing that $EQ_{CFG}$ is co-Turing-recognizable incorrect?
In this context, lexicographic order means:


First order by length.
Within each length, order lexicographically.


You're saying that the proof is incorrect, but in fact it is only inaccurate in that the order is not quite the lexicographic order. I would say that the proof has a small mistake, but is otherwise correct.

One often encounters such small issues in intricate mathematical arguments. Instead of immediately declaring failure when you run upon such a difficulty, you should try to see if the argument can be fixed by making small adjustments. You're not in a trial, acting as a prosecutor. Rather, you should believe the author that she had some valid proof in mind, but perhaps was a bit sloppy when trying to express her thoughts on paper. It's a cooperative game, in which you are trying to make the proof work rather than try to break it.