I booked my hotel in Nathan Road, Casa hotel. I want to go to the Lantau Island.

Lantau Island refers to a large area, which spot do you refer to?
Anyway, the MTR Tung Chung Line leads to the island, you can take the line to reach the island first, and then proceed your trip further.

From the hotel, you can walk to Yau Ma Tei Station to take the MTR Tsuen Wan Line to Lai King Station, where you can transfer to Tung Chung Line to Lantau Island. If going to Ngong Ping 360, the cable car can be taken nearby.