Colloquial. Almost always used with body parts that can hang: 耷拉着耳朵 (drooping ears), 耷拉着脑袋 (head down), 耷拉着眼皮 (drowsy eyelids). The second syllable is neutral tone (la), not lā.
memory
The 耳 (ear) radical in 耷 hints at the original sense - 'big ears that flop down'. Picture a sad-eared puppy.
