The current sheet structure modification by lower-hybrid drift instability (LHDI) has been shown to lead to quick magnetic reconnection triggering (QMRT) even in a thick current sheet (Tanaka et al., 2005). The three-dimensional simulations, however, have been limited to certain sets of parameters. Having learned which effects of LHDI are crucial for QMRT in these three-dimensional results, we perform a series of two-dimensional simulations of LHDI (reconnection itself not included) with various current sheet thickness D, guide field intensity B0y, and the frequency ratio τ (τ = ωpe/Ωe, where ωpe is the electron plasma frequency and Ωe is the electron gyrofrequency) and inspect how these parameters affect the QMRT process. While QMRT looked promising in the three-dimensional studies with B0y = 0 and τ = 1, the two realistic factors, nonzero guide field and τ larger than 1, requires rather small current sheet thickness for QMRT to be operative in the magnetospheric situations.