Most AVRs have a "delay" setting within the speaker setup menu that allows adjustment of either a global delay or a speaker-specific delay. This setting can be used to compensate for asymmetric speaker placement or to help with less than ideal room geometry.
When it comes to audio "lag" however, I think that most of those cases result from one or both of the following scenarios:
- Playing games on a modern flat-panel display that has all sorts of artificial image "enhancements" enabled - things like smooth motion/frame interpolation, noise reduction, etc.
- Connecting the game system directly to the TV, then using the TVs audio output to connect to an AVR (or frequently a low-end HTiB system that lacks the necessary inputs to connect it the "right" way) - this will automatically downmix the audio to analog stereo.
Both of these situations introduce extra "processing" to either the video or audio path of the game signal, which often introduces lag with the audio.
Connecting things to the AVR as you describe is a good idea - at least this way you know the audio and video signals should reach the AVR "in sync". Also, AVRs are designed to handle audio/video signals in just about any format imaginable, so no additional downmixing or processing is done (unless you specifically set up the device to do so).
If you do encounter any audio lag - attempt your fixes as far "downstream" as possible first (i.e. start with the TV, then move to the AVR, and finally, if all else fails, see if any in-game adjustments work). All things being equal, your TV is the most likely source of any delay/lag.