As you probably already know Latissimus dorsi produces a range of movements including extension and medial rotation of the shoulder joint, and also aids in lateral flexion of the trunk. What you might not know is that they also have a protective role through significantly increasing spinal stiffness via resisting flexion and protecting the LD (lumbo-dorsal) fascia against shear forces. Good core control, accompanied with coordinated co-contraction of musculature is essential when performing any movement, especially loaded movements, to avoid injury.
How does this apply to improving your deadlift?
Firstly a little anatomy lesson, your lats are connected to the thoracolumbar fascia (Lumbo-dorsal fascia) which is a thick layer of connective tissue that connects to the gluteal musculature, and also covers the lumbar spine and erector spinae muscles.
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The fibre orientation of the gluteal musculature and the contralateral portion of the latissimus dorsi are orientated in the same direction. So when lifting, the force is transferred upwards from the lower limbs through to the contralateral lats due to the fibre orientation of the musculature involved, forming an x shape belt of force lines across the back. Without adequate lat activation you are potentially leaving yourself open to injury and a substantial amount of force untapped.