The number of objects occupying orbital regimes beyond Geosynchronous Earth Orbit and cislunar space are expected to grow in the coming years; Especially with the Moon reemerging as latest frontier in the race for space exploration and technological superiority. In order to support this growth, new methods of autonomously navigating in cislunar space are necessary to reduce demand and reliance on ground based tracking infrastructure. Periodic orbits about the first libration point offer favorable vantage points for scientific or military spacecraft missions involving the Earth or Moon. This thesis develops a new autonomous spacecraft navigation method for cislunar space and analyzes its performance applied to Lyapunov and halo orbits around $L_1$. This method uses existing lunar ranging retroreflectors (LRRR) installed on the Moon's surface in the 1960s and 1970s. A spacecraft can make laser ranging measurements to the LRRR to estimate its orbit states. A simulation platform was created to test this concept in the circular restricted three body problem and evaluate its performance. This navigation method was found to be successful for a subset of Lyapunov and halo orbits when cycling the five measurement targets. Simulation data showed that sub-kilometer position estimation and sub 2 centimeter per second velocity accuracies are achievable without receiving any state updates from external sources. / Master of Science / The number of objects occupying the space between the Earth and Moon (cislunar space) is expected to grow in the coming years as the Moon regains popularity in the latest race for space exploration and technological superiority. In order to support this growth, new methods of determining a spacecraft's position and velocity while in this region of space are necessary to reduce demand and dependence on Earth based methods, which have historically relied upon. Repeating orbits around the equilibrium point between the Earth and Moon provide valuable observation points for scientific and military spacecraft missions. This thesis develops a new spacecraft navigation method for cislunar space and analyzes how well it performs in two different types of orbits, Lyapunov and halo orbits. This method uses existing laser reflector panels that were installed on the Moon's surface in the 1960s and 70s. A spacecraft can use these panels to make range or distance measurements in order to estimate its position and velocity. Software was written to simulate the motion of a spacecraft as it is acted on by gravity from the Earth and Moon. Different scenarios were then simulated and used to test this concept and evaluate its performance. Lunar laser ranging was found to be successful for a some Lyapunov and halo orbits when switching between the five different reflector panels on the Moon. Data generated from the simulations show that position can be estimated with errors less than SI{1}{kilo meter}, and velocity error on the order of a few centimeters per second, all without receiving any additional information from Earth based systems.