For the first time, hybrid molecules were synthesized on the basis of lithocholic and (5Z,9Z)-1,14-tetradeca-5,9-dienedicarboxylic acids, obtained in two stages using the homo-cyclomagnesiation reaction of 2-(hepta-5,6-diene-1-yloxy)tetrahydro-2H-pyran at the key stage. The resulting hybrid molecules containing 5Z,9Z-dienoic acids are of interest as novel synthetic biologically active precursors to create modern drugs for the treatment of human oncological diseases. The synthesized hybrid molecules were found to exhibit extremely high in vitro inhibitory activity against human topoisomerase I, which is 2–4 times higher than that of camptothecin, a known topoisomerase I inhibitor. Using flow cytometry and fluorescence microscopy, it was first shown that these new molecules are efficient apoptosis inducers in HeLa, U937, Jurkat, K562, and Hek293 cell cultures. In addition, the results of investigations into the effect of the synthesized acids on mitochondria and studies of possible DNA damage in Jurkat tumor cells are also presented.