The refraction index of the quantized lossy composite right-Left handed transmission line (CRLH-TL) was deduced in the thermal coherence state. The results show negative refraction index (herein the left-handedness) can be implemented by the electric circuit dissipative factors(i.e., the resistances R and conductances G) in the higher frequency bands (1.446GHz≤ ω ≤ 15GHz), and flexibly adjusted by the left-handed circuit components (C l , L l ) and the right-handed circuit components (Cr, Lr) at a lower frequency (ω=0.995GHz) . The flexible adjustment for left-handedness in a more wider bandwidth will be significant to the microscale circuit design for the CRLH-TL and may pave the theoretical preparation for its compact applications.