Analog Lagrange Coded Computing (ALCC) is a recently proposed computational paradigm wherein certain computations over analog datasets are efficiently performed using distributed worker nodes through floating point representation. While the vanilla version of ALCC is known to preserve the privacy of the datasets from the workers and also achieve resilience against stragglers, it is not robust against Byzantine workers that return erroneous results. Highlighting this vulnerability, we propose a secure ALCC framework that is resilient against a wide range of integrity threats from the Byzantine workers. As a foundational step, we use error-correction algorithms for Discrete Fourier Transform (DFT) codes to build novel reconstruction strategies for ALCC thereby improving its computational accuracy in the presence of a bounded number of Byzantine workers. Furthermore, capitalizing on some theoretical results on the performance of the DFT decoders, we propose novel strategies for distributing the ALCC computational tasks to the workers, and show that such methods significantly improve the accuracy when the workers' trust profiles are available at the master server. Finally, we study the robustness of the proposed framework against colluding attacks, and show that interesting attack strategies can be executed by exploiting the inherent precision noise owing to floating point implementation.