To understand why a long life puja is essential, we must understand the value of the Guru. He is our guide in this life, the bardo, and future lives. He is immensely important. It is not a case where if we ask him to live he will, and vice-versa, but that to offer such a ceremony purifies our own broken samayas.
–Geshe Lama Konchog
Requesting the guru to stay for a long time is part of the Seven-Limb practice. Because of the special relation between teacher and student, the student's request for the guru to stay long brings forth an auspicious dependent arising of the teacher's longevity.
Similarly, a Long Life Puja ceremony is a powerful practice with the following benefits:
It purifies broken samaya with the guru.
It is a cause for long life for attendees.
It builds a strong karmic connection with the guru.
It gives students potential to meet qualified spiritual masters in the future.
It leaves seeds in the student to achieve one of Buddha's 32 main characteristics.