An analytic theory of the localized edge modes (EM) in chiral liquid crystals (CLC) is developed. Equations determining the edge mode frequencies are found and analytically solved for the case of low decaying modes and solved numerically for the problem parameters values typical for the experiment. The discrete EM frequencies specified by the integer numbers n are located close to the stop band edge frequencies outside the band. The expressions for space distribution of the n's mode field in CLC layer and for its temporal decay are presented. The possibilities of reduction of the lasing threshold due to the anomalously strong absorption effect are theoretically investigated for a distributed feedback lasing in CLC. It is shown that a minimum of the threshold pumping wave intensity may be reached, generally, for the pumping wave propagating at an angle to the helical axes. However, for lucky values of the related parameters it may be reached for the pumping wave propagating along the helical axis. The lowest threshold pumping wave intensity occurs for the lasing at the first low frequency band-edge lasing mode and the pumping wave propagating at an angle to the spiral axes corresponding to the first absorption maximum of the anomalously strong absorption effect at the high frequency edge of stop band. The corresponding analytical study is performed for the case of the average dielectric constant of LC coinciding with the dielectric constant of the material limiting LC. Numerical calculations of the DFB lasing threshold at EM frequencies are performed for the typical values of the related parameters.