High-speed serial links are fundamental to energy-efficient and high-performance computing systems such as artificial intelligence, 5G mobile and automotive, enabling low-latency and high-bandwidth communication. Transmitters (TXs) within these links are key to signal quality, while their modeling presents challenges due to nonlinear behavior and dynamic interactions with links. In this paper, we propose LiTformer: a Transformer-based model for high-speed link TXs, with a non-sequential encoder and a Transformer decoder to incorporate link parameters and capture long-range dependencies of output signals. We employ a non-autoregressive mechanism in model training and inference for parallel prediction of the signal sequence. LiTformer achieves precise TX modeling considering link impacts including crosstalk from multiple links, and provides fast prediction for various long-sequence signals with high data rates. Experimental results show that LiTformer achieves 148-456$\times$ speedup for 2-link TXs and 404-944$\times$ speedup for 16-link with mean relative errors of 0.68-1.25%, supporting 4-bit signals at Gbps data rates of single-ended and differential TXs, as well as PAM4 TXs.