We propose MuseControlLite, a lightweight mechanism designed to fine-tune text-to-music generation models for precise conditioning using various time-varying musical attributes and reference audio signals. The key finding is that positional embeddings, which have been seldom used by text-to-music generation models in the conditioner for text conditions, are critical when the condition of interest is a function of time. Using melody control as an example, our experiments show that simply adding rotary positional embeddings to the decoupled cross-attention layers increases control accuracy from 56.6% to 61.1%, while requiring 6.75 times fewer trainable parameters than state-of-the-art fine-tuning mechanisms, using the same pre-trained diffusion Transformer model of Stable Audio Open. We evaluate various forms of musical attribute control, audio inpainting, and audio outpainting, demonstrating improved controllability over MusicGen-Large and Stable Audio Open ControlNet at a significantly lower fine-tuning cost, with only 85M trainble parameters. Source code, model checkpoints, and demo examples are available at: https://musecontrollite.github.io/web/.