This one is a weird one, as it depends on whether you upgraded to Lion or bought a new system running Lion out of the box.
If you upgraded, your running apps will have the glowing dot indicators you’re used to seeing in the dock. If you’re on a new Lion system, they won’t. With Apple trying to move to a persistent state/instant start app design model, these running indicators may eventually be unnecessary. For now, with the vast majority of apps still being designed for Snow Leopard and earlier, the lack of dots is just really confusing.
You can re-enable the dots under
System Preferences -> Dock -> Show indicator lights for open applications.