"need a lesson" is correct and usable in written English.
You could use this in a variety of contexts. For example, "I'm having trouble understanding algebra; I think I need a lesson."
"You don't need a lesson".
"Charles," he told him, "you need a lesson".
You plainly need a lesson from the Welsh government.
They need a lesson in competition, fair play and sportsmanship.
"You need a lesson like that, that you're not invincible".
Walking lessons can help correct your body's unintentional habits, even if you think you need a lesson in walking about as much as you need one in blinking.
"He needs a lesson," said another, who published pictures of Mr. Shashaa meeting with police officers.
"Apparently, President Obama needs a lesson in American history," he said.
Needed: A Lesson in Geography The actor JEREMY PIVEN was born in New York.
Clearly the headmaster, Chris Seward, needs a lesson or two about the essential right of privacy from his own pupils.
Here, I thought, is a man who has never thought about the free flow of traffic, and sorely needs a lesson in allowing New Yorkers some room to move.
