Abstract: To take full advantage of time-series ultra-high precision photometric data for about 800000 stars obtained during the Kepler space telescope’s mission in 2009-2018, the LAMOST telescope began to carry out low-resolution spectroscopic observations for stars in Kepler (K1) and K2 fields in 2012 and 2015, known as the LK1 and LK2 projects, respectively．After making stastistic analysis on the observed target coverage rates of the LK1 and LK2 projects the improvements of the two projects under better astronomical site conditions were predicted．Until June 2021, LAMOST’s coverage of the K1 sky area has reached 43%, and that of observable targets in the K2 sky area has reached 38%．If the seeing condition, sky background and observable night numbers could be improved at a new site, the coverage of LAMOST observations for K1 targets will reach 80% in two observational seasons, and that for K2 targets will reach 70% after four observational seasons．