This paper numerically and experimentally investigates and demonstrates the design of an optofluidic in-plane bi-concave lens to perform both light focusing and diverging using the combined effect of pressure driven flow and electro-osmosis. The concave lens is formed in a rectangular chamber with a liquid core-liquid cladding (L²) configuration. Under constant flow rates, the performance of the lens can be controlled by an external electric field. The lens consists of a core stream (conducting fluid), cladding streams (non-conducing fluids), and auxiliary cladding streams (conducting fluids). In the focusing mode, the auxiliary cladding stream is introduced to sandwich the biconcave lens to prevent light rays from scattering at the rough chamber wall. In the diverging mode, the auxiliary cladding liquid has a new role as the low refractive-index cladding of the lens. In the experiments, the test devices were fabricated in polydimethylsiloxane (PDMS) using the standard soft lithography technique. Ethanol, cinnamaldehyde, and a mixture of 73.5% ethylene glycol and 26.5% ethanol work as the core stream, cladding streams and auxiliary cladding streams. In the numerical simulation, the electric force acts as a body force. The governing equations are solved by a finite volume method on a Cartesian fixed staggered grid. The evolution of the interface was captured by the level set method. The results show that the focal length in the focusing mode and the divergent angle of the light beam in the diverging mode can be tuned by adjusting the external electric field at fixed flow rates. The numerical results have a reasonable agreement with the experimental results.