The absolute L subshell specific electron impact ionization cross sections near the ionization threshold (16 < E < 45 keV) of Lead and Thorium are obtained from the measured L X-ray production cross sections. Monte Carlo simulation is done to account for the effect of the backscattered electrons, and the final experimental results are compared with calculations performed using distorted wave Born approximation and the modified relativistic binary encounter Bethe model.The sensitivity of the results on the atomic parameters is explored. Observed agreements and discrepancies between the experimental results and theoretical estimates, and their dependence on the specific atomic parameters are reported.