This study focuses on the preparation of carbon fiber precursors from solutions of cellulose in N-methylmorpholine-N-oxide with the addition of bis(trimethylsilyl)acetylene, studying their structural features and evaluating thermal behavior. The introduction of a silicon-containing additive into cellulose leads to an increase in the carbon yield during carbonization of composite precursors. The type of the observed peaks on the differential scanning calorimetry (DSC) curves cardinally changes from endo peaks intrinsic for cellulose fibers to the combination of endo and exo peaks for composite fibers. For the first time, coefficient of thermal expansion (CTE) values were obtained for Lyocell fibers and composite fibers with bis(trimethylsilyl)acetylene (BTMSA). The study of the dependence of linear dimensions of the heat treatment fibers on temperature made it possible to determine the relation between thermal expansion coefficients of carbonized fibers and thermogravimetric curves, as well as to reveal the relationship between fiber shrinkage and BTMSA bis(trimethylsilyl)acetylene content. Carbon fibers from composite precursors are obtained at a processing temperature of 1200 °C. A study of the structure of carbon fibers by X-ray diffraction, Raman spectroscopy, and transmission electron microscopy made it possible to determine the amorphous structure of the fibers obtained.