A method for constructing Marks' decahedral lattice for the studies of Lennard-Jones cluster structures is proposed. With the proposed method, clusters with Marks' decahedral structure are studied up to the size 10 000. By comparing the energies of these Marks' decahedral structures, the growth sequences with different structural characteristics, denoted by the term "family", are investigated. It is found that the structures with lowest energies are not always attributed to the even families; odd families also provide the structures with lowest energies. Therefore, a new lowest energy sequence is proposed.