The table is basically wrong. The header says "I want to license my code under LGPL v2.1" so the answer is "no". Including the possibility of a relicense completely muddles things and rather defeats the purpose of the table. If you already own the copyright, as is assumed for the top header, then you can relicense it to whatever you want.
It's basically answering the question "I want to license my code under LGPL v2.1, can I?" with "sure, but you have to use a different licence than LGPL v2.1".
It isn't even assuming that you own the GPL v2 code. If you read the paragraph above it explicitly says
It assumes that someone else has written some software under one of these licenses, and you want to somehow incorporate code from that into a project that you're releasing (either your own original work, or a modified version of someone else's software).
I think the purpose of the odd corner case is that you can relicense someone else's LGPL v2.1 code into GPL v2. But in that case you could just look at the LGPL v2.1 -> GPL v2 entry in the table.