"These sleeping dogs won't lie, as opposed to "let sleeping dogs lie" meaning:
1.To avoid starting old conflicts
2.Not to disturb a situation as it is
So "These Sleeping Dogs won't lie" means:
1.Some kind of conflict continues and "rears it ugly head"
Example: These sleeping dogs won't lie can be said about:
1.An issue that is still unsettled
2.Conflict between countries etc.