I'm currently investigating about this, and I know something that may help you.
Did you try installing glipper? To install it, simply open synaptic and search for it, and install it, or you can do it from a terminal with the following command:
Once the package is installed, right-click the gnome-panel and press "Add to panel", then select Clipboard manager.
sudo apt-get install glipper
You will see a small clipboard icon that appears there, that is glipper, the clipboard manager.
Now, try once again to copy an URL with links2 -g, and afterwards, check if it is shown in the glipper drop-down menu. If it is shown, simply select it, and now will be the clipboard's active object, meaning that you can paste it with ctrl+v.
I hope that helps!
I'm not an expert on clipboard issues, but I think this inconvenient might happen due to some incompatibilities of links2 (or terminal-based apps in general) and the X clipboard.