I want to distribute a header only library and I think that the spirit of the LPGL license is very much what I want. In particular, however, I want that a 3rd party that uses my library and modifies it, shares these changes. Does the LGPL license, and if so which versions, cover this requirement?
No free licence can require that someone who modifies your library share those changes; see eg this answer for more discussion of that issue.
What LGPLv3 will do for you is require that if anyone modifies your library, and they distribute the modified library either on its own or as part of an executable program (proprietary or otherwise), they must make the source of the modified library available to those downstream recipients, and they must license it under LGPLv3, or GPLv3, when they do so (LGPLv3 s2).
The practical upshot of this is that the changes they make end up being available to the community, and if they're LGPLv3-licensed, you'll be able to incorporate them back into your library.
Will that suffice?