I am not a lawyer, but from my understanding of the GNU Lesser General Public License 3.0, section 4 explicity excludes static linking as the requirement states:
You may convey a Combined Work under terms of your choice that, taken together, effectively do not restrict modification of the portions of the Library contained in the Combined Work and reverse engineering for debugging such modifications, if you also do each of the following:
(Emphasis mine.)
Section 4d.0 is not possible by the nature of Android APKs: the APK is compiled to Dex and signed as a whole, containing referenced libraries, and hence swapping out libraries cannot be done without the original source code, the keystore and keystore password.
Section 4d.1 may be possible by deploying two APKs:
- One APK containing the LGPL library and in turn open source and licensed under LGPL
- Another proprietary APK referencing the LGPL application.
Deploying such an application, however, is not possible directly through Google Play without specifically adding the requirement that the user proceed to download the LGPL dependency, which would need to be deployed as a separate application on Google Play. This would be very tedious for the end user, and realistically isn't an option for a typical consumer application.
As per the discussion with Prof. Falken in William Tate's answer, the terms of the LGPL may be more applicable to C libraries included through native code, as they reside inside the APK as a separate library. Although the APK cannot be signed, it is possible to repack the APK with the object file replaced. From my perspective, that technically fits the requirements of the license.