Hi Richard,
Good question, and lots of good answers. Modern practice is to follow the order of the circle of fifths. But that was not always the case. So, indeed, depends on your historical context. Bach was writing in G sharp for the WTC, and it was most certainly not intended to be enharmonic with A flat. But if you look at18C manuscripts and JS Bach in particular there is wide variance in how key signatures were done, and Bach often repeated the notes in the signature, say having two c sharps, for reasons of his own (quite interesting to see). Obviously his music teacher would fail him today. This was before the age of standardization of everything.
So I would discard advice about rewriting in A flat. G sharp is perfectly good, even though the textbooks call it a 'theoretical key' - what they mean is that it is hard to read when an alternative is available in an equal tempered context. As Urs has said, there are plenty of valid musical contexts for a key such as G sharp.
Since lilypond gives you the ability to change the ordering in the key signature, you ahve complete freedom in what you do.
Nothing new here, but I just wanted to chime in on this interesting topic.