How long will a willow tree live for?

As with people, it depends. They are, according to all the experts, short-lived outside their native China. They grow fast and reach maturity at about 10-12 years. If they haven't been pruned (preferably yearly), they will start to suffer from problems with their bark and branches, so that they will need to be cut back severely .. or down! They are also prone to attack by pests (presumably chiefly in their early years) by pests and fungal types and are moderately intolerant of drought. Look for problems in winters after 10+ years when heavy horizontal branches are prone to split at the crotch where they meet the trunk.