I am not convinced

I am not sure log(K) guesses is needed to find the lie.

In case that there is certainly a false statement in the first 7 questions, ceil(log(7))=3 guesses are required. However, there may be a lie in the last 3 questions or none at all. At least 4 guesses are needed to find the lie.

If log(K) guesses is the number of guesses needed to find the lie, the formula should be
K = ceil(log(N)) + ceil(log(K))
By substituting K = 10, the right side of the equation results 11.