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In this work we present the results of our analysis of 16,300 medium-resolution LAMOST spectra of late-type stars in the Kepler field with the aim of determining the stellar parameters, activity level, lithium atmospheric content, and binarity. We have used a version of the code ROTFIT specifically developed for these spectra. We provide a catalog with the atmospheric parameters (Teff, log(g), and [Fe/H]), radial velocity (RV), and projected rotation velocity (vsini). For cool stars (Teff < 6500 K), 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 14,300 spectra of 7443 stars. Literature data were used for a quality control of the results. The Teff and log(g) values are in good agreement with the literature. The [Fe/H] values appear to be overestimated for metal-poor stars. We propose a relation to correct the [Fe/H] values derived with ROTFIT. We were able to identify double-lined binaries, stars with variable RVs, lithium-rich giants, and emission-line objects. Based on the H-alpha flux, we found 327 active stars. We detected the LiI-6708 line and measure its equivalent width for 1657 stars, both giants and stars on the main sequence. Regarding the latter, we performed a discrete age classification based on the atmospheric lithium abundance and the upper envelopes of a few open clusters. Among the giants, we found 195 Li-rich stars, 161 of which 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 explanation of the enrichment of Li in our sample. The fraction of Li-rich giants, about 4%, is higher than expected.