Humans learn to recognize and manipulate new objects in lifelong settings without forgetting the previously gained knowledge under non-stationary and sequential conditions. In autonomous systems, the agents also need to mitigate similar behavior to continually learn the new object categories and adapt to new environments. In most conventional deep neural networks, this is not possible due to the problem of catastrophic forgetting, where the newly gained knowledge overwrites existing representations. Furthermore, most state-of-the-art models excel either in recognizing the objects or in grasp prediction, while both tasks use visual input. The combined architecture to tackle both tasks is very limited. In this paper, we proposed a hybrid model architecture consists of a dynamically growing dual-memory recurrent neural network (GDM) and an autoencoder to tackle object recognition and grasping simultaneously. The autoencoder network is responsible to extract a compact representation for a given object, which serves as input for the GDM learning, and is responsible to predict pixel-wise antipodal grasp configurations. The GDM part is designed to recognize the object in both instances and categories levels. We address the problem of catastrophic forgetting using the intrinsic memory replay, where the episodic memory periodically replays the neural activation trajectories in the absence of external sensory information. To extensively evaluate the proposed model in a lifelong setting, we generate a synthetic dataset due to lack of sequential 3D objects dataset. Experiment results demonstrated that the proposed model can learn both object representation and grasping simultaneously in continual learning scenarios.