The example sentence would be...
Mike spent all weekend doing the assignment, but he lost it on his way to school. It's back to the drawing board for him.
I usually use this idiom to show that something was a failure. In your example English sentence the reason he had to start again was not because it was a failure, but because he lost it.
I think this sentence is still ok, but in general the reason they start again is because it doesn't work.
"From scratch" means "from the very beginning".
Excellent answer!
Good job
