Vertical farming systems (VFS) represent an innovative approach within controlled environment agriculture, addressing challenges in traditional horizontal farming by facilitating precise monitoring of plant growth in controlled settings. This approach indeed enables the optimization of environmental factors such as light, temperature, and nutrient supply, ultimately enhancing crop productivity, land use efficiency, and production cycle management. This study focuses on assessing the impact of plant density on light absorption competition and the influence of light quality on crop dry weight development—critical aspects throughout the entire life cycle of protected cultivations. To evaluate and control these growing conditions, the study present a mathematical growth model for lettuce tailored to VFS. The model employs ordinary differential equations to simulate the dynamic behavior of non-structural and structural dry weight, as a function of incident photosynthetically active radiation, carbon dioxide concentration, air temperature, light quality, and crop density. The model defines the light use efficiency coefficient through a linear combination of light spectrum components, incorporating terms to address interactions among different light bands. The extinction coefficient, describing light interception efficiency by the plant canopy, is defined as a smooth decreasing function of Leaf Area Index (LAI), representing increasing competition among plants over time. The calibration of the model employed data from destructive experiments on three lettuce varieties conducted over 40 days, under different densities and light quality conditions. The study also explores the potential of machine learning for generalizing the parameter estimation to unanalyzed lettuce varieties. The proposed model's performance is showcased in this work, emphasizing its sensitivity to parameters defining the light use efficiency and the extinction coefficients. The proposed model provides a more accurate representation of the vegetative growth for the analyzed lettuce varieties compared to models neglecting photon spectrum effects and competition for light absorption.