Magnetic resonance imaging (MRI) is a leading modality for the diagnosis of liver cancer, significantly improving the classification of the lesion and patient outcomes. However, traditional MRI faces challenges including risks from contrast agent (CA) administration, time-consuming manual assessment, and limited annotated datasets. To address these limitations, we propose a Time-Conditioned Autoregressive Contrast Enhancement (T-CACE) framework for synthesizing multi-phase contrast-enhanced MRI (CEMRI) directly from non-contrast MRI (NCMRI). T-CACE introduces three core innovations: a conditional token encoding (CTE) mechanism that unifies anatomical priors and temporal phase information into latent representations; and a dynamic time-aware attention mask (DTAM) that adaptively modulates inter-phase information flow using a Gaussian-decayed attention mechanism, ensuring smooth and physiologically plausible transitions across phases. Furthermore, a constraint for temporal classification consistency (TCC) aligns the lesion classification output with the evolution of the physiological signal, further enhancing diagnostic reliability. Extensive experiments on two independent liver MRI datasets demonstrate that T-CACE outperforms state-of-the-art methods in image synthesis, segmentation, and lesion classification. This framework offers a clinically relevant and efficient alternative to traditional contrast-enhanced imaging, improving safety, diagnostic efficiency, and reliability for the assessment of liver lesion. The implementation of T-CACE is publicly available at: https://github.com/xiaojiao929/T-CACE.