Lambert's problem is a boundary value problem that arises in preliminary mission design, where orbital transfers must be determined given orbital location and a prescribed time-of-flight. The related equations are non-invertible and have traditionally been solved using iterative methods. In this work, we study the bounded one-revolution elliptic Lambert problem and propose a neural-surrogate approach that combines geometry-aware normalization with the prediction of the transfer semi-major axis. The normalization maps transfer instances with geometry-dependent admissible ranges into a common canonical representation, on which a multilayer perceptron (MLP), DeepONet, and Kolmogorov-Arnold Networks (KAN) are trained and compared. Among the tested models, the MLP achieves the highest predictive accuracy, while the structured architectures provide an alternative view of the normalized solution space. In Earth-Mars and multi-planetary flyby case studies, the surrogates preserve the broad features of the classical solutions and identify promising transfer regions.