You are the sole author of library A, formerly released under MIT, and currently released under LGPL. A is used by project B, in which you and developer Carol are the sole rightsholders. You wish to relicense A under GPL.
I fear a fork is imminent. If you relicense A to GPL, the joint project it depends on will either have to use only pre-existing, MIT/LGPL-licensed versions, or re-license under the GPL. Assuming Carol chooses the former, at that point there will be parallel versions of A and B under development, distributed under different licences.
Going forward, the hard work is almost all going to be on Carol's side: any improvements you make in A or B will need to be clean-room re-engineered by Carol in order to add to his/her non-GPL fork of A or B respectively. Meanwhile, any improvements Carol makes to his/her version of B, you may promptly incorporate in your version.
This sort of thing does happen. Some might say it's a shame, but it seems part of the licence ecosystem to me. We'll see how dedicated Carol is to non-copyleft licensing when you're able to reuse all of his/her changes with nearly no effort, when the reverse will very much not be true.
Edit: if you want Carol to be able to continue to use A without making any licence changes to B, leave A LGPL. As we have said before, do not under any circumstances try to invent your own licence. The uncertainty alone will cause people to avoid your library.
In any case, the strategy doesn't work. Here's a thought experiment for your licence above: I take the code to B, and remove all but a not-quite-de-minimis amount of the content, then create on that an almost-entirely new work, D, which being a copyright derivative of B, can also use library A on non-GPL terms. Now my friend Eric takes D, removes the last vestiges of B, and creates a work F, which being a copyright derivative of D, and thus of B, can also use A on non-GPL terms, even though F is completely different from B. To permit it to one+derivatives is to permit it to all.
If you really want A to be GPL, re-license, and risk B failing. If you really want B to succeed, leave A as LGPL.