The Rope Snake is Lucas' Grab attack. He can also use it as a Tether Recovery.
It is also one of his taunts.
In MOTHER 3, Lucas did not use a Rope Snake; the item actually belonged to Duster.
Tactically speaking, the Rope Snake is an excellent move to use because players often do not expect a tether recovery from Lucas. It's also longer than people give it credit for (slightly shorter than Ivysaur's Vine Whip).