Does asbestos exposure always lead to lung cancer?

No: Asbestos is mostly associated with a cancer of the lining of the lung or chest wall (the pleura) called mesothelioma.

Asbestos: Despite the known link to the rarer mesothelioma, more non-small cell lung cancers are caused than that. There is benign conditions called asbestosis associated as well, and mostecposure causes nothing. To complete the circle, we find mesothelioma without asbestos exposure. Lorillard made kent cigarettes with a "micronite" filter of asbestos fibers. Double whammy, but burned poorly.

Short answer...: No. While asbestos increases the risk of lung cancer, most exposed individuals don't get lung cancer or any of the other problems linked to asbestos. Think of it like this, most traffic deaths occur in people in cars, but most people who drive/ride in cars don't die in accidents. Not the perfect analogy, but it helps convey the difference between exposure to a risk factor and getting the disease.