In protecting cultural heritage, deacidification is used to stabilize acidic papers, ensuring the neutralization of acids present in the paper. But in the process of aging, several mechanisms of degradation occur simultaneously. Therefore, substances used to stabilize the paper should contain an antioxidant component in addition to the deacidifying component. The effect of the antioxidant (hindered amine light stabilizers—HALS type) on the stabilization of lignin-containing acid papers during accelerated aging was studied in this work. The effective deacidification component was magnesium; the solvent was hexamethyldisiloxane (HMDSO). The 4-amino-2,2,6,6-tetramethylpiperidine series of hindered amine light stabilizers (HALS) was selected as appropriate for creating a modifying system based on HMDSO. The modification system was tested on samples of a model test acid lignin-containing paper (NOVO) and naturally aged acidic paper from the real book. The addition of substances to the proposed deacidification system has a favorable effect on stabilizing the pH during aging and provides the inhibition of the oxidative degradation products and stabilization of the cellulose degree of polymerization. It was confirmed that the application of the system containing deacidification and an antioxidant component may increase the effectiveness of the protection of acid groundwood paper heritage objects. Adding a tested antioxidant to the proposed deacidification system has a favorable effect on stabilizing the pH value for a long time in accelerated aging.