Lucius (and Draco) at first thought Harry might be a Dark wizard.
J.K. Rowling addresses this in a writing on Pottermore. Especially before Harry actually became part of the wizarding world at 11, one of the reasons that the wizarding world suspected could be why he survived the attack was that he might be a Dark wizard in the making himself.
Many different theories had been in circulation for years as to how Harry survived what should have been a lethal attack, and one of the most persistent was that Harry himself was a great Dark wizard. The fact that he had been removed from the wizarding community seemed (to wishful thinkers) to support this view, and Draco’s father, wily Lucius Malfoy, was one of those who subscribed most eagerly to the theory. It was comforting to think that he, Lucius, might be in for a second chance of world domination, should this Potter boy prove to be another, and greater, pure-blood champion. It was, therefore, in the knowledge that he was doing nothing of which his father would disapprove, and in the hope that he might be able to relay some interesting news home, that Draco Malfoy offered Harry Potter his hand when he realised who he was on the Hogwarts Express.
- Draco Malfoy (Pottermore)
Originally thinking Harry might be a new Dark wizard, both Draco and Lucius would have considered it worthwhile to at least try to build a relationship with him (until of course they see how wrong the thought was). While this theory may seem unusual, Lucius wasn’t the only one who thought it was possible. We see more evidence that some people in the wizarding world believed this theory when Ernie Macmillan tells some fellow Hufflepuffs that must be how Harry survived after people learned that Harry could speak Parseltongue when he spoke to the conjured snake in the duel.
“Ernie lowered his voice mysteriously, the Hufflepuffs bent closer, and Harry edged nearer so that he could catch Ernie’s words.
‘No one knows how he survived that attack by You Know Who. I mean to say, he was only a baby when it happened. He should have been blasted into smithereens. Only a really powerful Dark Wizard could have survived a curse like that.’ He dropped his voice until it was barely more than a whisper, and said, ‘That’s probably why You Know Who wanted to kill him in the first place. Didn’t want another Dark Lord competing with him. I wonder what other powers Potter’s been hiding?”
- Harry Potter and the Chamber of Secrets, Chapter 11 (The Duelling Club)
This belief was short-lived, at least for the Malfoys. Once he actually met Harry, Draco soon realized that Harry was certainly not an ally, and would not be the next Dark Lord to seize control and possibly bring the Malfoys power.
Harry’s refusal of Draco’s friendly overtures, and the fact that he had already formed allegiance to Ron Weasley, whose family is anathema to the Malfoys, turns Malfoy against him at once. Draco realised, correctly, that the wild hopes of the ex-Death Eaters – that Harry Potter was another, and better, Voldemort – are completely unfounded, and their mutual enmity is assured from that point.
- Draco Malfoy (Pottermore)
When Lucius actually meets Harry, we see no evidence that he once had such high hopes for what Harry might be - but he would have had a year of hearing from his son Draco what Harry was like.