Amycus panicked and wanted to redirect the Dark Lord’s wrath.
Amycus likely didn’t think his plan through entirely. Once he felt that Alecto pressed her Dark Mark and had summoned the Dark Lord, me immediately attempted to find her, and grew increasingly panicked as he went and found that she didn’t have Harry and was Stunned.
“I dunno, do I? Shut it!’ snarled an uncouth voice that Harry knew was that of the Carrow brother, Amycus. ‘Alecto? Alecto? Are you there? Have you got him? Open the door!”
- Harry Potter and the Deathly Hallows, Chapter 30 (The Sacking of Severus Snape)
He realized that if the Dark Lord came and they didn’t have Harry to hand over to him, he’d be furious with them, and they’d be faced with whatever punishments he chose.
“ALECTO! If he comes, and we haven’t got Potter – d’you want to go the same way as the Malfoys? ANSWER ME!”
- Harry Potter and the Deathly Hallows, Chapter 30 (The Sacking of Severus Snape)
He was very afraid of what the Dark Lord might do to Alecto if he got there to see she’d called him with no reason. His main concern was how angry the Dark Lord would be, so he was desperate to find a way to get the Dark Lord not to direct his anger at Alecto. Blaming the students, though it was unlikely to work, would have absolved her of any blame.
“She’s only Stunned,’ said Professor McGonagall impatiently, who had stooped down to examine Alecto. ‘She’ll be perfectly all right.’
‘No she bludgering well won’t!’ bellowed Amycus. ‘Not after the Dark Lord gets hold of her! She’s gorn and sent for him, I felt me Mark burn, and he thinks we’ve got Potter!”
- Harry Potter and the Deathly Hallows, Chapter 30 (The Sacking of Severus Snape)
Though lying to the Dark Lord, a skilled Legilimens, wasn’t a good plan, Amycus wasn’t particularly intelligent, and was also panicking. The Dark Lord was already on his way there, so Amycus had needed to think of something quickly, and that was the best he had come up with.