indicators are usually things like ph levels or the results of chemical reactions. These are not living.
However, living indicators are indicators that are living.. lol like indactor species (animal indicators), e.g. nymph stone fly is an indicator for low pollution levels and rat tailed maggots are an indicator of high pollution levels..
Skin cancer is also a living indicator since cells cause skin cancer and cells are living..
Lichen springs to mind. Basically a living species which has a measurable reaction in response to environmental conditions (air pollution etc.). I think mayfly (or mayfly larvae) is another one.