Lamprocapnos spectabilis (L.) Fukuhara is a perennial plant species valued in the horticultural, cosmetic, and pharmaceutical markets. To date, however, there were no studies on tissue culture systems in this species when adjusted from non-meristematic explants. The aim of this study is to induce callogenesis, organogenesis, and somatic embryogenesis in non-meristematic explants of Lamprocapnos spectabilis ‘Alba’ cultured in various media and to analyze the chemical diversity of the produced callus. Leaf, petiole, and internode explants were cultured on the modified Murashige and Skoog (MS) medium fortified with various combinations and concentrations of 6-benzyladenine (BA), indole-3-acetic acid (IAA), 1-naphthaleneacetic acid (NAA), 2,4-dichlorphenoxyacetic acid (2,4-D), and picloram (PIC). After 10 weeks of culturing, the morphogenetic response of explants was evaluated and the concentration of chlorophylls, carotenoids, anthocyanins, and polyphenols in callus was analyzed. There was no influence of explant type on the callogenesis efficiency (62.1–65.3%). The highest fresh weight of callus was produced on leaf explants in the presence of 2,4-D or PIC. In contrast, the highest share of dry weight was found in internode-derived calli and cultured on IAA-supplemented medium (up to 30.8%). Only 2.5% of all explants regenerated adventitious shoots, while rhizogenesis was reported in 4.5% of explants. Somatic embryos were produced indirectly by 0% to 100% of explants, depending on the culture medium and explant type. The highest mean number of embryos (11.4 per explant) was found on petioles cultured in the MS medium with 0.5 mg·L−1 BA and 1.0 mg·L−1 PIC. Calli cultured in media with NAA usually contained a higher content of primary and secondary metabolites. There was also a significant impact of explant type on the content of anthocyanins, polyphenols, and carotenoids in callus. Further studies should focus on the elicitation of metabolites production in callus culture systems of the bleeding heart.