Hamilton won his fifth world title this year after comfortably seeing off the challenge of Vettel.
However, Mercedes had to complete the second half of the season without Lauda in their pits after he fell seriously ill.
The Austrian legend required a lung transplant and has since undergone long, intensive rehabilitation.
The 69-year-old has returned home in time for Christmas and in one of his first interviews since returning to full health, he spoke extremely highly of Ferrari ace Vettel, who sent him a touching letter.
“The letter written by Sebastian, in his own hand, was a great pleasure for me, full of fine words and affectionate considerations,” Lauda told La Gazzetta dello Sport.
“I didn’t expect it, usually drivers don’t do these things, they just drive. But he’s a good person.
“He has had moments of discouragement, we know.
“But it would be absurd to question him. He will recover, a champion will not forget how to drive.
“He’ll come back strong as ever and he’ll still be Hamilton’s rival in 2019.”
Lauda was frustrated not being present as Hamilton lifted his latest Drivers’ Championship, which takes him two titles behind the great Michael Schumacher’s record.
But he was still able to keep up with the team through various ways.
“I didn’t miss a single grand prix, even though I was in the company of so many IV,” he added.
“I watched all the races, called the pits on the weekends, and they always told me what was going on.
“It was like being on the edge of the track with the others. I have to say that I, once again, discovered the warmth of the people I’ve been working with for years.”
Lauda also revealed how tough his recovery process was.
“I knew it would be hard, very hard,” he said.
“In such conditions I could only do one thing, fight. I did it for every moment, I’m still doing it.
“Being within my own four walls is something else.
”The air here is cleaner, the climate is not as bad as in Austria.
“In a month, they told me, I should be fully fit and ready to start again. I’ll follow the grands prix as before. Why not?”