Dropbox normally uses a silent-but-deadly approach to handle its updates. Basically it installs it automatically for you sometime within a week or so of the new release. But would it kill Dropbox just to give you an alert and let you know that it's ready? Especially for a big change like restoring the Dropbox submenu in Lion?
Here's how you can manually upgrade without waiting for Dropbox to catch up. First confirm that you are running an earlier version. Dropbox > Preferences > Account reports the current version.
Next, head on over to the install page and download the 1.1.40 installer. Open the dmg. Quit your earlier Dropbox install and drag the new version into Applications. Then launch the updated app and Bob's your uncle.
If you're one of the few dozen people who have been using my GrabUpper utility to generate URLs while waiting for Dropbox to catch up to Lion, you'll be pleased to know that the utility continues to work with the 1.1.40 release. It will monitor your Dropbox folder and create URLs whenever you drop something in.
For everyone else, you can revert to using the contextual pop-up menu (Right-Click > Dropbox > Copy Public Link) now that it finally works on Lion.