lay a hand on = hit someone
If you ever try to lay a hand on me, I'll hurt you.
Never lay a hand on a child.
lay off / (be or get) laid off = to lose a job because business is slow.
Even though he was a good worker, he was laid off because the company wasn't doing very well. (passive voice)
look (it) up = to find information
If you need to find a good price on a car, you can look it up on the internet.
You can also look up information in a book.