The mechanical properties of the cellular microenvironment play a crucial role in modulating cell function, and many pathophysiological processes are accompanied by variations in extracellular matrix (ECM) stiffness. Lysyl oxidase (LOx) is one of the enzymes involved in several ECM-stiffening processes. Here, we engineered poly(ethylene glycol) (PEG)-based hydrogels with controlled mechanical properties in the range typical of soft tissues. These hydrogels were functionalized featuring free primary amines, which allows an additional chemical LOx-responsive behavior with increase in crosslinks and hydrogel elastic modulus, mimicking biological ECM- stiffening mechanisms. Hydrogels with elastic moduli in the range of 0.5–4 kPa were obtained after a first photopolymerization step. The increase in elastic modulus of the functionalized and enzyme-responsive hydrogels was also characterized after the second-step enzymatic reaction, recording an increase in hydrogel stiffness up to 0.5 kPa after incubation with LOx. Finally, hydrogel precursors containing HepG2 (bioinks) were used to form three-dimensional (3D) in vitro models to mimic hepatic tissue and test PEG-based hydrogel biocompatibility. Hepatic functional markers were measured up to 7 days of culture, suggesting further use of such 3D models to study cell mechanobiology and response to dynamic variation of hydrogels stiffness. The results show that the functionalized hydrogels presented in this work match the mechanical properties of soft tissues, allow dynamic variations of hydrogel stiffness, and can be used to mimic changes in the microenvironment properties of soft tissues typical of inflammation and pathological changes at early stages (e.g., fibrosis, cancer).