Precise forecasting of cancer outcomes is essential for medical professionals to assess the well-being of patients and develop customized therapeutic plans. Despite its importance, achieving precise forecasts remains a formidable challenge. To tackle this issue, we present an innovative method that harmonizes the Grey Wolf Optimizer (GWO) with Levy flight to optimize the weights and biases of a Backpropagation (BP) neural network-a prominent machine learning model extensively employed in classification tasks. Our novel approach, LGWO-BP, is tailored to augment the precision of cancer prognosis predictions. We performed comparative analyses against other methodologies across various functions and public datasets to assess their effectiveness. The experimental results show the exceptional strengths of the proposed LGWO-BP method, particularly its accuracy and reliability compared to GWO-BP, and show that it achieves comparative results against state-of-the-art (SOTA) methods. Our assessment of the LGWO-BP technique's efficacy involved undertaking empirical tests across half a dozen openly accessible datasets. For the early-stage diabetes dataset, LGWO-BP achieved an accuracy of 0.92, a recall of 0.93, a precision of 0.88, an F1-score of 0.91, and an AUC of 0.95. Utilizing the diabetes dataset from 130 U.S. hospitals, the LGWO-BP algorithm achieved a precision rate of 0.97, a sensitivity of 1.00, a correct classification rate of 0.99, a harmonic mean of precision and recall (F1-score) of 0.98, and an area under the ROC curve (AUC) of 1.00. For the diabetes health indicators dataset, LGWO-BP achieved an accuracy of 0.9 and an AUC of 1. Leveraging data from The Cancer Genome Atlas (TCGA) - a U.S.-led initiative conducting in-depth molecular research to elucidate the causative mechanisms of cancer - this study focuses on three specific cancer types within the dataset: lung, breast, and esophageal cancers. TCGA provides a rich repository of genomic, transcriptomic, epigenomic, and patient-specific clinical data across 33 cancer types. In evaluating the prognostic performance of the LGWO-BP (Lévy flight-enhanced Grey Wolf Optimizer integrated with Back Propagation) model, we observed AUC (Area Under the Curve) scores of 0.70 for miRNA expression, 0.72 for gene expression, and 0.72 for DNA methylation. Regarding precision, the model achieved accuracies of 0.67, 0.69, and 0.66 for miRNA expression, gene expression, and DNA methylation, respectively. For recall, the corresponding values were 0.71, 0.61, and 0.62. Notably, the F1-scores, which balance precision and recall, were 0.69 for miRNA expression, 0.65 for gene expression, and 0.62 for DNA methylation. This research not only advances the application of machine learning in medical prognosis but also offers crucial guidance for clinicians in developing more precise and reliable prognostic tools for cancer patients. By enhancing the efficacy of machine learning-driven cancer prognosis, our proposed LGWO-BP approach has the potential to improve patient care and treatment outcomes significantly.