The Ph.D. would be the doctoral degree. The LP is:

LP or NCPsyA
The licensed psychoanalyst has obtained his license from the state department of education (requirements vary from state to state). Recipients must have a master's degree or higher, and completed psychoanalytic study in a program deemed qualified by the state DOE. The LP must complete a supervised psychoanalysis program and pass a state-certified examination. (New York State Department of Education)