Spike cameras have shown great potential in capturing ultra-high-speed motion scenes by mimicking the retinal fovea's function, especially addressing the challenges of full-time imaging and high dynamic range in an energy-efficient fashion. Leveraging spike emission mechanisms, these cameras achieve extraordinary temporal resolutions in terms of thousands of frames per second, far surpassing traditional imaging devices. However, the resulting data, characterized by its large scale and sufficient temporal imaging nature, poses significant challenges for storage and transmission. In this paper, we propose an advanced lossless compression model for spike data via constructing a novel spike data representation scheme. We first introduce an efficient short-term aggregation method for spike sequences, paired with an intensity remapping technique to mitigate the effects of noise inherent in the spike sampling approach. In addition, we design and propose the Categorical Logit-based Entropy Model (CLEM) by quantitatively and precisely measuring the required code length of the underlying representation to generate an implicit representation that models the unique statistical distribution of spike data. We leverage these findings to introduce a novel learned lossless spike compression model that significantly reduces the data rate while preserving full data fidelity. Extensive experimental results on PKU-Spike-Recon and more real-world spike datasets demonstrate that our approach achieves state-of-the-art (SOTA) performance, with competitive computational complexity. The proposed method illuminates a new path towards lossless compression without encoding the prediction residual for spike data coding.