> IANAL but GPL does state that you can relicense under any other later version of the license
No. Both the GPL and the LGPL encourage you to add the “or any later version” clause that allows the FSF to retroactively add other licensing options to your code, but they do not include that clause themselves. The standard example is that the SMB protocol implementations in the Linux kernel (GPL 2.0 only) and the Samba project (GPL 3.0 or later) cannot share code in either direction.
> LGPL states that it counts as GPL 2.1
Also no. The GNU Lesser General Public License (LGPL) 2.1 (says that it) counts as the successor of the GNU Library General Public License (LGPL) 2.0, not of the ordinary GNU General Public License (GPL) 2.0. GPL 2+ code cannot be treated as LGPL 2.1, and from the FSF’s perspective allowing that would not make sense, as GPL 2 enforces strictly more copyleft than LGPL 2.1.
Why the confusing renaming? As far as I can see, Stallman wanted library authors to switch from LGPL to GPL, so that library users are forced into the GPL as well. The chosen solution was to play language games to redefine the “L” in “LGPL” to mean “lesser” instead of “library”. There is an official article that explicitly points out this piece of manipulation[1], but I still cannot suppress the vague feeling of revulsion at being manipulated.
[1] https://www.gnu.org/licenses/why-not-lgpl.html