Ages ago I started a thread on airport lounges with kids. I was somewhat curious and wanted feedback for my article so it was interesting getting the skinny from those of you with experience.
One good point that was made was that there was more room in the restrooms for changing, etc. It's also a bit more secure as far as your things are concerned and dealing with crowds.
Some of you mentioned specific lounges where there were actual children's areas.
Another comment mentioned delays, where the lounge is a sanity-saver, with or without kids!
If you have access to the lounge, you might want to take advantage for the above reasons. If the baby is asleep in the stroller, go for it! But also consider the infant rooms at your airport, as well as play areas. That might be easier with a very active 9 monther.