They've got their lines crossed (8)
I believe the answer is:
mongrels
'they've got' is the definition.
I can't tell whether this defines the answer.
'lines crossed' is the wordplay.
I cannot quite see how this works, but
'lines' could be 'els' (el is a kind of line) and 'els' is found within the answer.
This may be the basis of the clue (or it may be nonsense).
'their' is the link.
Can you help me to learn more?
(Other definitions for mongrels that I've seen before include "Dogs of mixed breed" , "Dogs of mixed breeds" .)