I've just upgraded to OS 10.7.3 and Docksend in Transmit 4 by Panic no longer works. I drop files on the dock icon and nothing happens in Transmit.
I used the Using DockSend help menu and it worked like a charm for me. I'm on 10.7.3 as well:
You might just need to toggle it off, wait (perhaps reboot) and toggle it back on. Here are detailed instructions from the help menu:
So, following that, you'll end up here:
Make sure that Use DockSend checkbox is checked! If it is and it still won't work, I would reinstall Transmit. If it still won't work after that, definitely contact Panic support.