fastest and cheapest way to go to Lantau Island if I'm coming from Tsim Sha Tsui with an elderly?

The best way is to take MTR Tsuen Wan line to Lai King Station. Then, change to Tung Chung Line to Tung Chung Station. The trip takes about 40 minutes, and the fare totals HKD 16.5. :) If your destination is Ngong Ping 360, take the cable car onto the top then. It is suitable for the elderly. No worry!