For anyone who is confronted with the same problem:
All you have to do is make sure you still have a pre-Lion system with EyeTV (2.5.3) on it, where you can let it complete the auto-tune process once and configure your channels. Afterwards, you just transfer the com.elgato.eyetv.plist in the /Library/Preferences/ folder from the old system to your Lion installation. This should make eyeTV keep that channel configuration permanently even under Lion. And apart from that, EyeTV 2.5.3 seems to really run surprisingly well.