is "linger on" means "stay for a long time?

Not necessarily--to linger on means to stay longer than is (or seems to be) necessary, or to stay after a condition is met. Someone might linger on at a park after a picnic is over, staying in the park after everyone else has gone home. You might cook a dish with garlic in it, and the smell of the cooked garlic might linger on even after the food has been eaten.

How long "linger on" refers to depends on the context. It might not mean a lont time at all.