In this paper, the nonautonomous Lenells-Fokas (LF) model is studied with the bilinear method and symbolic computation. Such analytical solutions of the nonautonomous LF model as one-soliton, two-soliton, and earthwormons are derived. Nonautonomous characteristics are then symbolically and graphically investigated, and it is finally found that the soliton velocity is time-dependent, and there exist soliton accelerating and decelerating motions. Further, two necessary conditions for the occurrence of earthwormon acceleration and deceleration (and their alternation) are pointed out.