lsusb lists the fingerprint reader in the x240 as follows:
Bus 002 Device 003: ID 138a:0017 Validity Sensors, Inc.
There exists experimental driver support for this in a fork of libfprint for vfs5011 sensors, however you'll need to compile the driver yourself. To get the fingerprint sensor to work for lightdm login, su etc, follow these steps.
sudo add-apt-repository ppa:fingerprint/fingerprint-gui