Owing to its antibacterial, anti-inflammatory, and antioxidant activities, in the last few years, lavender essential oil (LVO) has been used in medical applications as a promising approach for treating infected wounds. However, the practical applicability of LVO is limited by its high volatility and storage stability. This study aimed to develop a novel hybrid hydrogel by combining phytic acid (PA)-crosslinked sodium alginate (SA) and poly(itaconic anhydride-co-3,9-divinyl-2,4,8,10-tetraoxaspiro[5.5] undecane (PITAU) and evaluate its potential effectiveness as an antibacterial wound dressing after incorporating LVO. The influence of the mass ratio between SA and PITAU on the properties and stability of hydrogels was investigated. After LVO loading, the effect of oil addition to hydrogels on their functional properties and associated structural changes was studied. FTIR analysis revealed that hydrogen bonding is the primary interaction mechanism between components in the hybrid hydrogels. The morphology was analyzed using SEM, evidencing a porosity dependent on the ratio between SA and PITAU, while LVO droplets were well dispersed in the polymer blend. The release of LVO from the hydrogels was determined using UV-VIS spectroscopy, indicating a sustained release over time, independent of the LVO concentration. In addition, the hybrid hydrogels were tested for their antioxidant properties and antimicrobial activity against Gram-positive and Gram-negative bacteria. Very good antimicrobial activity was obtained in the case of sample SA_PITAU3+LVO10% against S. aureus and C. albicans. Moreover, in vivo tests showed an increased antioxidant effect of the SA_PITAU3+LVO10% hydrogel compared to the oil-free scaffold that may aid in accelerating the healing process of wounds.