M'learned readers have already proposed several explanations for Lincoln's empty chair: that it signifies his approachability; the fact that his life was cut short; his disdain for the political systems of Ancient Rome (possibly a bit of a stretch, this one) or his skill at oratory. I'm most impressed by all these theories, though I still think it looks a bit silly.
One correspondent also wonders when and why a statue of an American hero came to be erected in Parliament Square. A little poking around reveals it was unveiled in 1920, having been delayed by the First World War, and was intended to celebrate the hundredth anniversary of the Treaty of Ghent in 1814, and thus peace between English speaking nations. (Tangent: Has this peace been maintained for the subsequent ninety years, I wonder? I certainly can't think of a war since between nations with English as their first language.)
Also, there was some disagreement about which of two statues to present. In the end, the less favoured one was sent to Manchester, where it still stands. Because in it Lincoln looks rather gaunt and haggard (even for him) and has his arms crossed over his abdomen, it became known as the Stomach Ache, or the Tramp With The Colic.
(In this statue, Lincoln has no chair. How the people of Manchester are expected to tell how good an orator he was, or how much he hated Rome, I have no idea.)