The most recent scholars (Donal O'Sullivan and Grainne Yeats, among others) cite Cornelius Lyons' birthplace as Macroom in Cork, and they are probably more reliable sources than O'Neill, whose book was written about a century ago in America and who had to rely a great deal on secondary sources. A lot of information has come to light since then, so I would go with Yeats & O'Sullivan who have seen the historical records first hand.

Also, remember that there are a fair number of Lyonses in Ireland (a glance at the Munster phone directory shows nearly a page of them: it's not an uncommon surname) and Cornelius is not a particularly unusual first name for that period, so you need to do more research before assuming that your Cornelius Lyons is the same man as the harper-composer. The first thing is to ascertain whether or not he had children, which will probably require the services of a professional genealogist.

Still, it would be a total gas if it turns out he IS your ancestor so please do keep us posted -