i think for most practical purposes documentation should have the same license as the code, because when code is changed, documentation may need to be changed accordingly.
don't use the fdl, as it will cause difficulties to include the manual in debian.
since some source files have different licenses, perhaps the manual sections related to those files could have the same license (not sure if that is practical) otherwise the lgpl may be sufficient (since linking does not really apply, there is no difference between the two i think)
the main aim should be to allow people who take bits of nettle can take the related documentation as well (like in pikes example) without causing a licening confusion in the resulting combination.
greetings, martin.