We have established and released a new stellar index library of the CaII triplet, which serves as an indicator for characterizing the chromospheric activity of stars. The library is based on data from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Low-Resolution Spectroscopic Survey (LRS) Data Release 9. To better reflect the chromospheric activity of stars, we have defined new indices R and R+. The library includes measurements of R and R+ for each CaII infrared triplet (IRT) from 699348 spectra of 562863 F, G, and K-type solar-like stars with a signal-to-noise ratio higher than 100, as well as the stellar atmospheric parameters and basic information inherited from the LAMOST LRS catalog. We compared the differences between the three individual indices of the CaII triplet and also conducted a comparative analysis of R_{lambda}8542_^+^ to the CaII H and K S and R_HK_^+^ index databases. We observe the fraction of less active stars decreases with Teff and the fraction of more active stars first decreases with decreasing temperature and turns to increase with decreasing temperature at 5800K. We also find that a significant fraction of stars that show a high activity index in both CaII H and K and IRT are binaries with low activity; some of them could be discriminated in the CaII H and K S index and R_{lambda}8542_^+^ space. This new stellar library serves as a valuable resource for studying chromospheric activity in stars and can be used to improve our comprehension of stellar magnetic activity and other astrophysical phenomena.