Potential energy surface calculations have predicted the existence of the island of triaxial strongly deformed (TSD) nuclei with N~94 and Z~72. Experimental discoveries of TSD bands have been first reported in Lu. Subsequent calculations indicated that Hf would be the most favorable even-even nuclei in the island region for finding low-lying TSD structures. However, experimental investigation of Hf nuclei performed with Euroball and Gammasphere produced negative results on the two nuclei. In the Gammasphere experiment three TSD bands were discovered in the main reaction product Hf. This success motivated an extension of the search for TSD bands in the region to heavier Hf-isotopes and neighboring Lu-isotopes. In order to search for TSD bands and the characteristic wobbling mode in Lu, the experiment using Sb ( Ca, xn) reaction was performed in Lawrence Berkeley National Laboratory (LBNL) with Gammasphere. Based on coincidence data acquired in the experiment, a new level structure for Lu was developed. Compared to level schemes in previous work, previously observed bands were extended to higher spins. Four new bands were assigned to Lu for the first time, and one of them was identified as a triaxial strongly deformed (TSD) band.