In the example cited above, it does not sound correct to say ""the child had a morbid propensity to tell lies", whereas your default, " "the child had a pathological propensity to tell lies?", is correct. We have a term called, "a pathological liar", and your default phrase would be readily understood.
We do use "morbid" in the following contexts :
1) "morbidly obese" (to imply a condition to a degree that can illicit serious disease or death)
2) morbid curiosity (imply an unnatural fascination of death and situations surrounding death)
A person with "morbid curiosity" hangs around the site of major car accidents or disasters. Also, one might describe a certain environment to have "a morbid ambiance", and describe as "morbid" various situations, like a scene in a movie.