This work presents a theoretical study, based on DFT calculations, about the changes induced when diatomic molecules (CO, O-2 and H-2) are adsorbed on defective (8,0) SWCNT doped with a Li atom. The adsorption of one Lithium atom is tested inside and outside of the nanotube containing a single vacancy. The Li atom induces a magnetic moment on the nanotube and an important reduction in its the band gap (E-g). The adsorption energy values (E-ads) for CO, O-2 and H-2 when Li is located inside, are higher than when Li is outside. The H-2 adsorption does not change the magnetic nature of the system. However, the CO and O-2 molecules reduce the magnetic moment from 1.0 mu(B) to 0.0 mu(B). The band gap energy is reduced for CO and O-2, while increases in the case of H adsorption. The work function (WF) value is reduced in the cases of CO and H-2; whereas for O-2 we observed an opposite behavior, then the final charge state of this molecule is negative. Based on our results, the system Li + defective (8,0) SWCNT can be proposed as possible candidate as gas sensor of CO,O-2 and H-2.