Publicly traded companies can make money by selling shares, also called stocks, to investors through the stock market. The supply and demand for stocks are affected by a number of factors, such as company and #039 financial performance, market trends, geopolitical events, and economic conditions. This study investigates the effectiveness of a new Meerkat-Optimized Long-Term Memory (LSTM) model in predicting stock prices and compares its performance with traditional LSTM, bidirectional LSTM (Bi-LSTM), and stacked LSTM models. Our approach involves the integration of an optimization technique based on the Meerkat algorithm with an LSTM model specifically designed to improve the adaptability and accuracy of complex nonlinear models of stock market data. The study uses a comprehensive dataset that includes various stock market indices and includes important price indicators such as open, close, high, low, and volume data. We use a robust evaluation framework that uses metrics such as mean absolute error (MAE), root mean square error (RMSE), and directional accuracy to evaluate and compare the forecasting abilities of models. This advance highlights the possibility of integrating biologically-influenced optimization algorithms with neural network models for financial time series forecasts, providing insights for developing more sophisticated and accurate forecasting tools for financial market analysis.