Peristaltic motions are used in a variety of industrial and real-world problems such as pumping mixture with such a high solid content from the mining sector, biogases, sewers facilities, food flow through the gastrointestinal system, urinary tract, and fallopian tube of human females where extremely abrasive, gritty, and viscous fluids are present. The goal of this theoretical study is to examine the impact of the lubricated walls on the peristaltic transport of a viscous fluid in an asymmetric medium. The interfacial condition is derived under the assumptions of thin film lubrication and long wavelength approximation. The theory of a dynamical system is utilized to examine the lubrication effects on the position and bifurcation of stagnation points in the flow. For this, three flow distributions, backward flow, trapping, and augmented flow, are discussed. The obtained system of equations is solved numerically by the shooting method based on Newton–Raphson root-finding algorithm in Mathematica. The prime findings for the velocity profile, pressure increase, trapping, and reflux criteria are illustrated through graphs. Bifurcation occurs earlier by increasing the influence of lubrication. The trapping area diminishes and the augmented flow section expands with the lubrication parameter. This will be useful for medical engineering, industrial and physiological systems. The comparison for the particular case of no-slip condition is presented and found to be in excellent agreement. [ABSTRACT FROM AUTHOR]