The aim of this work was to determine the effect of stress conditions caused by different light sources, i.e., blue LED (λ = 430 nm), red LED (λ = 670 nm), blue and red LED (70%:30%) and white LED (430–670 nm) on the growth and morphology of cultivated in vitro Dracocephalum forrestii shoot culture. It also examines the effects on bioactive phenolic compound production and photosynthetic pigment content, as well as on antioxidant enzyme activity (CAT, SOD, POD) and antioxidant properties. The most beneficial proliferation effect was observed under white LEDs (7.1 ± 2.1 shoots per explant). The white and blue lights stimulated the highest fresh weight gain, while red light induced the highest dry weight gain. The total phenolic acid content ranged from 13.824 ± 1.181 to 20.018 ± 801 mg g DW−1 depending on light conditions. The highest content of rosmarinic acid was found in the control shoots (cultivated under fluorescent lamps), followed by culture grown under red light. All LED treatments, especially red and blue, increased salvianolic acid B content, and blue increased apigenin p-coumarylrhamnoside biosynthesis. The greatest ferric reduction activity was observed in shoots cultivated under red light, followed by blue; this is associated with the presence of the highest total phenol content, especially phenolic acids. Similarly, the highest DPPH radical scavenging potential was observed under red light followed by blue. This study proves that LEDs have emerged as significant support for directed in vitro propagation, taking advantage of specific stress responses on various light spectra. This study also showed how stress induced by different LED light spectra increases in Dracocephalum forrestii the synthesis of pharmacologically-active compounds. Hence, light stress may turn out to be a simpler alternative to metabolic engineering for improving the production of secondary metabolites of therapeutic value.