I have software licensed under LGPL 2.1 and I want to modify it and re-publish the whole software under the GPL 3.0 license. Is this legally possible?
I think so, but I'm not completely sure.
LGPL 2.1 says
...3. You may opt to apply the terms of the ordinary GNU General Public License instead of this License to a given copy of the Library. To do this, you must alter all the notices that refer to this License, so that they refer to the ordinary GNU General Public License, version 2, instead of to this License. (If a newer version than version 2 of the ordinary GNU General Public License has appeared, then you can specify that version instead if you wish.) Do not make any other change in these notices. ...