Lambert's problem plays a significant role in preliminary design phases of many space missions. In this paper, an analysis of techniques for the solution of Lambert's problem on graphical processing units (GPUs) is presented. Two algorithms including Universal Variables and Gooding's algorithm are executed on both the CPU and GPU and are compared in terms of accuracy, robustness, and performance. Lambert's problem solvers are implemented as MATLAB scripts, serial mex, parallel mex with a parfor loop, and CUDA C functions. It is found that the choice to implement an algorithm on the CPU or GPU does not affect accuracy and robustness. However, for the considered test cases, the implementation of Gooding's algorithm on the GPU is found to be 275 times faster than the method of Universal Variables on the CPU. Furthermore, the time to initialize the GPU and transfer data from the CPU was compared to the time to solve Lambert's problem. For small input sizes, the data transfer time is the dominating factor in both algorithms, so the improvement in the speed of computation with GPU has more of an effect for large input sizes. Lastly, techniques to optimize thread and block settings are presented. The developed technique is utilized to generate the so-called porkchop plots for Earth-to-Mars targeting over a certain window for launch time and time of flight.