License compatibility is a one-way street. If A-licensed software can link to B-licensed software, this does not imply that linking in the reverse direction is allowed.
The LGPL-2.1 has one-way compatibility with the GPL-2+:
- 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.
You can therefore only license code under the LGPL-2.1 if you can also license it under GPL-2+.
The incompatibility of Apache-2 and GPL-2 is well documented. If your software is a combined/derivate work with/of Apache-2 software, you cannot license that software under the GPL-2 and therefore cannot license it under the LGPL-2.1 either. I wish the LGPL would have made this relationship clearer, and the LGPL-3 does clarify this.
Note that the LGPL-2.1 is permissive only with regards to software that uses this library, which is defined as:
- A program that contains no derivative of any portion of the Library, but is designed to work with the Library by being compiled or linked with it, is called a "work that uses the Library". Such a work, in isolation, is not a derivative work of the Library, and therefore falls outside the scope of this License.
I.e. this permissiveness only applies to downstream works, not to upstream works like an Apache-2 library that your software uses: the upstream dependency is neither derivative of your library, nor was it designed to work with your library.
The GPL FAQ item What legal issues come up if I use GPL-incompatible libraries with GPL software? mentioned by Philippe Ombredanne discusses that you can provide an exception to the GPL-2 for linking with incompatibly-licensed upstream libraries, provided that you are the copyright holder. It is reasonable to believe that this can also be done for LGPL-2.1 licensed software, and that these exceptions would not affect the GPL-2 compatibility in section 3: the exceptions would survive the license change.
If the copyright owners of an LGPL-2 licensed software explicitly add an incompatible dependency, this could be interpreted as an implied license exception. However, you should avoid relying on implied licenses since they might not be accepted in all jurisdictions.
I disagree with the interpretation that absent an explicit exception, you could add an incompatible dependency without being the sole copyright owner.
You do not have the right to issue an explicit or implied exception since you are bound by the terms of the LGPL-2, so you cannot add an incompatibly-licensed dependency.
If there are examples existing libraries that have done this, these do not provide a precedent that would allow you to ignore the terms of the LGPL-2.