Last weekend in Baku, triple world champion Hamilton was moved to clarify quotes that suggested he might retire at the end of this season.
Now, Mercedes team chairman Lauda backed Hamilton's denial, saying that the original comments were "misunderstood".
"He is staying, of course, because he has a contract," the F1 legend told German broadcaster Sky. "He is not Nico [Rosberg]!"
In fact, Lauda says that Hamilton is not only staying in 2018, but already pushing for a new deal beyond that.
"Lewis is already discussing the contract extension with us," said the Austrian. "He has asked about it.
"He is highly motivated, as are we, even though negotiations are yet to start.
"But I must honestly say, I feel a tremendous respect for him. From the very beginning of the season he has this fighting spirit, he is in excellent physical condition, and the results are growing from race to race."
Hamilton is currently second in the driver rankings, trailing leader Sebastian Vettel by 14 points.