Nonlinear evolution equations (NLE-Es) arise in a variety of domains, including fluid dynamics, biological sciences, the study of solid states, optical fibres, coastal engineering, ocean physics, and nonlinear complex physical systems. This work examines the Lie symmetry study of the Benney-Luke (B-L) equation relying on two nonzero real parameters. The Lie infinitesimal generators, the one-dimensional optimal system, and the geometric vector fields are all obtained using the Lie symmetry technique. To start, we find close-form invariant solutions by employing symmetry reduction of Lie subalgebras. In some reduction cases, we transform the B-L equation into a variety of non-linear ordinary differential equations (NL-ODEs), which have the benefit of providing a significant number of closed-form solitary wave solutions. The traveling wave solutions contain special functional parameter solutions, trigonometric function solutions, rational function solutions, and hyperbolic trigonometric function solutions. The dynamical profile of closed-form wave solutions exhibits periodic solitons, dark peakon solitons, bright solitons, and bright solitons (bell shape) which we reveal in our study for the first time. By using Noether’s method, we also determine the conservation laws. Finally, three-dimensional diagrams are used to reveal the dynamical investigation of some known solutions.