They are actually running through a heavily wooded area near the Turtle Bay Resort where numerous other scenes are filmed for Lost.
The Turtle Bay Resort is located near Oahu's most northerly point. You can drive northeast from Haleiwa on the Kamehameha Highway or approach it from the other direction where it is about 10 minutes past the Polynesian Cultural Center in La'ie.
If you're not a guest at the Turtle Bay Resort, you may be asked to pay a fee to park. There is a security gate that you must pass to reach the resort. They can't refuse you entrance since all beaches in Hawaii must have public access. Past the golf course and tennis courts to the left, you can spot the horse stables. After you park you'll want to head in that direction and follow the markers for the west/green trail which will take you through numerous filming locations for Lost. You can print a copy of the trail map here.
View a screenshot of this location from ABC's Lost.
