Any hope for my lemon tree?

I have no idea about the age of my lemon tree. It was here when I purchased the property 6 years ago. When I first moved in, lemons were plentiful.















A year ago most of the leaves fell off, but it still was producing

lemons. The local garden center suggested a dose of 16-4-2, which did not really help. Today most of the new growth dies off. The leaves turn brown at the tips and existing branches appear die back from the tip. Does my lemon tree have a disease, is it just old or is neglect to blame?