No, you are not.
As a rule of thumb, only the copyright holder (i.e., the author of your third-party library) is allowed to change the license under which code is distributed.
There is a weird exception in the GPL, but it doesn't help you: the FSF has historically encouraged that software be licensed under the GPLv2 or later. Specifically, in most cases, you will find the following in the
LICENSE file or equivalent:
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
This means that GPLv2 code can be used in a GPLv3 project without incident.
Unfortunately, there is no clause, either in the GPLv2 or GPLv3, for using an earlier version of the GPL. You'll either need to convince the GPLv2 project to upgrade to GPLv3 or avoid the GPLv3 library.