Let sleeping dogs lie means to leave an old problem alone rather than stir it up. Better to let sleeping dogs lie, I would let sleeping dogs lie, we should let sleeping dogs lie.
It is advice about timing rather than truth, since the problem is real and the point is that raising it costs more than it gains. The image needs no explaining, which is why the phrase has survived for centuries.
1phraselet sleeping dogs lieTo leave an old problem alone rather than stir it up again.
“I wanted to ask about their old quarrel, but I decided to let sleeping dogs lie.”
let sleeping dogs lie is an advice.
A piece of folk wisdom attested in English from the nineteenth century, with the image self-explanatory.
Attestations exist from the 1820s and 1830s. Earlier ones may be discoverable with better corpus searches. The metaphor is self-evident and is typical of folk wisdom. To choose to pass by a sleeping dog without stirring it is comparable to letting a hornets' nest or beehive be, not poking a bear, and so on.
Etymology from Wiktionary, CC BY-SA
Practised in Idioms