The raise of dynamic workloads and on demand provision of resources to the end users is a major challenge in cloud environment. Despite of many techniques are available to resolve the challenge still it lags. Hence, in the paper proposed a novel framework by integrating Long Short-Term Memory (LSTM) model for workload prediction and Sine Cosine Algorithm (SCA) for efficient task scheduling. The proposed LSTM model for workload prediction is trained using real time Google 2019 Cluster Trace dataset from the Kaggle source. The model achieved strong performance with mean Squared Error (MSE) of 0.0021 indicating accurate actual and predicted workload forecast. The predicted workload is passed to Sine Cosine Algorithm (SCA) for optimal Task-to Virtual Machine (VM) mapping and also minimizing the key parameters of defined Fitness function: Makespan, Energy Consumption and Load Imbalance. The results of the proposed model outperforms the subsisting models with makespan reduction of 17.5%, reduced energy consumption of 20.7% and improved performance in load balance from 0.49 to 0.37. The integration of LSTM-SCA framework provides robust model with accurate solution for efficient workload-aware and efficient task scheduling in the cloud environment.