In a recent article, Mac tech site Cult of Mac has said that Apple appears to no longer be supporting USB modems and other analog forms of communication in OS X. Apparently in Lion if you plug in an Apple USB modem, the system will give you an error claiming the hardware is unsupported, and that you cannot use the modem with your computer. While this may be the case with Apple's modem, others seem to be working just fine.
Apple may be eager to phase out modems in favor of more modern options, but so far support for them has not been completely removed from the system. On seeing the Cult of Mac article I dug out my old Diamond Supra Express 56K modem from a box in my closet, and attached it to my system running Lion to see what would happen. I expected perhaps there would be an error, but did not see anything, and upon checking saw the modem was recognized and listed in the Network system preferences.
Entering a phone number and clicking to connect gave the familiar buzzing dialing sounds that unfortunately will not work over my VoIP telephone service, but for all it's worth, the modem appears to be working and interfacing with the system just fine.
Thinking perhaps this could perhaps be an issue with leftover modem configurations when upgrading my system from Snow Leopard, I took a look at the Lion installer to see if any modem configurations are available there. Browsing through the installer using the package manager Pacifist showed the presence of the "SM56KUSBAudioFamily.kext" kernel extension, which contains the audio and modem family extensions within it. In addition, the /Library folder contains a Modem Scripts directory that holds a number of modem configurations for devices from numerous manufacturers.
If for some reason your modem is not working, try checking for the kernel extension I mentioned above in the /Macintosh HD/Library/Extensions/ folder, and also see if there are any script files in the /Macintosh HD/Library/Modem Scripts/ folder. If for some reason these resources are missing from your system, then you might try reinstalling OS X.
To reinstall Lion, first make a backup of your system using Time Machine or a drive clone, and then boot to the recovery partition by restarting with the Command-R keys held down. In the installer, choose the option to install OS X Lion, which you can then use to reinstall Lion over your existing installation, downloading the necessary install files from Apple's online servers.
This option does require you to have an Internet connection, but if you have created your own Lion install disc or flash drive or have purchased an official OS X install drive, then you can use those installers without needing to download files from the Internet.
Wi-Fi and cellular broadband connectivity are vastly overtaking previous-generation options; however, the need for modems is still here, to the extent that fax systems are still broadly used. While Apple is a progressive company and constantly pushes people to adopt new and modern standards, there is still enough use of modems for Apple to support the technology in OS X, at least for now. Nevertheless it appears that Apple's USB modem is out of the pool of options for Lion users. If you need a modem that will work in Lion, the Zoom 3095 and the U.S. Robotics USR5637 are a couple of options that should work.
Update (August 17, 12:48pm): MacFixIt reader John wrote in mentioning the Apple modem uses a unique driver that was written in 32-bit code, and therefore will not load in the default 64-bit kernel that Lion runs. To get the modem working in Lion, you have the option to boot to 32-bit mode by restarting your computer and boot it with the "3" and "2" keys held down, which will load the 32-bit kernel. Alternatively you can apply some hidden system settings (see this article) to force the system to always boot to the 32-bit or 64-bit kernel.