There are specific updates to Elgato software that are designed for use with OS X 10.7 (Lion):
Elgato Video Capture 1.1.1
EyeConnect 1.6.11
EyeTV 3.5.3
Turbo.264 HD 1.2
These versions, or any higher version, should work as expected with the latest update to OS X.
You can get these latest updates here: