Question
In October of last year my lawn care company applied lime to my lawn 2 times within 2 weeks.A short time after that I noticed my tree roots showing and some bare spots especially around the trees.Also where I took the dog out the soil was really soft and muddy and the grass died.I've been taking the dog out for 10 years and it never did anything to the grass.Could the lime have caused this?

Answer
Lime is applied to raise the pH of the soil; or lower the acidity (it's the same thing). Ideally it should be incorporated in the top 6" for best result.
I do not know why this would have to be done twice in two weeks. You can ask them.
It is hardly likely that the limestone application by itself caused the symptoms which you describe.