Low-dose CT (LDCT) imaging is preferred in many applications to reduce the object's exposure to X-ray radiation. In recent years, one promising approach to image reconstruction in LDCT is the so-called optimization-unrolling-based deep learning approach, which replaces pre-defined image prior by learnable adaptive prior in some model-based iterative image reconstruction scheme (MBIR). While it is known that setting appropriate hyper-parameters in MBIR is challenging yet important to the reconstruction quality, it does not receive enough attention in the development of deep learning methods. This paper proposed a deep learning method for LDCT reconstruction that unrolls a half-quadratic splitting scheme. The proposed method not only introduces learnable image prior built on framelet filter bank, but also learns a network that automatically adjusts the hyper-parameters to fit noise level and the data for processing. As a result, only one universal model needs to be trained in our method to process the data taken under different dose levels. Experimental evaluation on clinical patient dataset showed that the proposed method outperformed both conventional and deep-learning-based solutions by a large margin.