The GPL does not require you to release the modified program. You are free to make modifications and use them privately, without ever releasing them.
But if you release the modified version to the public in some way, the GPL requires you to make the modified source code available to the users, under the GPL.
Thus, the GPL gives permission to release the modified program in certain ways, and not in other ways; but the decision of whether to release it is up to you.
So if you modify LWP, and you release it, it has to be under the GPL (Update:considering LWP being released under the GPL; I don't know how it works under Artistic License)
Greetz
Beatnik
... Quidquid perl dictum sit, altum viditur.