I translated this as "The dogs lose their way"... lose "the" way sounds weird. If I heard that, I wouldn't really know what the speaker meant.
So, what does this really mean?
that they can't find THE (specific?) road, or
that they have lost their way (i.e. they are physically lost, or metaphorically no longer doing what it is they believe in).
To me this sentence sounds like the dogs were tracking something (a person or an animal) and then they lost the scent trail. Is this a context that this sentence would be used in, or is there some other way people might more normally express that idea? I know דרך is used figuratively a lot, but tracking dogs would seem an appropriate enough context for the literal usage.
How about "the dogs get lost?" Does "לאבד את הדרך" mean something different from "ללכת לאיבוד"?