Proverbs are fixed expressions, their wording does not change even though the individual words might seem interchangeable at first glance. "Let the sleeping dogs lie" is one such fixed phrase, and it carries the meaning that you should avoid reopening a matter that has already settled down, because stirring it up again could cause fresh problems.
The other three choices try to confuse the reader by rearranging the same words or twisting the meaning of lie into telling a falsehood. "Sleeping dogs tell lies" shifts the meaning entirely and is not a real saying. "Dogs sleeping lie till late" and "Lie sleeping dogs till the dawn comes" simply scramble the word order into ungrammatical, meaningless sentences, they do not exist as idioms.
Since a proverb must match its accepted form exactly, the answer has to be option 4, Let the sleeping dogs lie.