In this work we present the results of our analysis of 16300 medium-resolution LAMOST spectra of late-type stars in the Kepler field aimed at the determination of the stellar parameters, activity level, lithium atmospheric content and binarity. We have used a purposely developed version of the code ROTFIT for the determination of the stellar parameters by adopting a grid of spectra of real stars. We provide a catalog with the atmospheric parameters (Teff, logg, and [Fe/H]), radial velocity (RV), and projected rotation velocity (vsini). For cool stars (Teff<6500K), we also calculated the H-alpha and LiI-6708 equivalent width, which are important indicators of chromospheric activity and evolutionary stage, respectively. We have derived the RV and atmospheric parameters for 14300 spectra of 7443 stars. Literature data (mainly from high- or medium-resolution spectra) were used for a quality control of the results and to assess the accuracy of the derived parameters. The Teff and logg values are in good agreement with the literature, although their distribution displays some clustering effect, which can be the result of the non-uniform distribution of the templates in the parameter space. The most relevant differences are found for [Fe/H], which appears to be overestimated for metal poor stars; this is also likely caused by the template grid. We propose a relation to correct the [Fe/H] values derived with ROTFIT. We were able to identify interesting objects, such as double-lined binaries, stars with variable RV, lithium-rich giants, and emission-line objects. Based on the H-halpha flux, we found 327 active stars. We could detect the LiI-6708 line and measure its equivalent width for 1657 stars both giants and on the main sequence. Regarding the latter, we performed a discrete age classification based on their atmospheric lithium abundance and the upper envelopes of a few open clusters. Among the giants we found 195 Li-rich stars, 161 are reported here for the first time. No relationship is found between stellar rotation and lithium abundance, which allows us to rule out merger scenarios as the predominant ones to explain the enrichment of Li in our sample. The fraction of Li-rich giants, about 4%, is higher than expected.