Yes, a Lama's longevity depends on the disciple's conduct. It is true. If the disciples are not doing what the Lama teaches, not following the instruction the Lama gives, then there's no necessary to have a Guru. And the Lama will find a way and reincarnate to a place where Dharma and the teaching is more needed and practiced.
But since this statement came out from H.H Dalai Lama's mouth, now question asked, "Does H.H Dalai Lama's longevity depends on his disciple's conduct or Dorje Shugden?" If it depends on his disciple's conduct, then what about the statement he made before, saying that Dorje Shugden practice will shorten his life? He even said there are monks in the monastery still practicing Dorje Shugden. So? Which is true? If Dorje Shugden is not the main reason that will shorten his life, then may H.H The 14th Dalai Lama swiftly announce that the ban on Dorje Shugden is lifted. Announce that, hospitals, schools, public places like hotels, restaurants should not discriminate Dorje Shugden practitioners and chase them out from their shop. Because of his announcement of the ban, has already created load of discrimination, segregation, separation, and fights. Recently he's slowing unveiling many things he said was contradicting.