Lincoln was never a Senator. He lost his senate race to his arch rival Stephen Douglas.
DOH!
Moreover, Lincoln never ran against Seward or any Senator from New York.
He won the 1860 election against Stephen Douglas (the real Senator from Illinois in the race), and the incumbent President John Breckinridge from Kentucky, with a 4th candidate from Tennessee thrown in for good measure.
So actually she was wrong in pretty much every detail.