"Is there a way to create an optical transistor that runs using a cheap laser and made using mirrors and lenses?" Yes and no. It depends on the definition of "cheap", and on how fast the "transistor" needs to be. Mirrors and lenses per se won't do anything but steer and concentrate light. You need a nonlinear medium, as @EmilioPisanty pointed out. There are some nonlinear media available that a talented home experimenter could use, such as fluorescent media, photothermoplastic media, and photochromic media. Perhaps easier, though, would be to play with optical feedback into the laser. Many lasers become unstable if a significant portion of their output is reflected directly back into the laser; and that instability could be treated as one optically switchable state of the laser. Nonlinear optical effects require a high power density, but a 50mw laser (which can be pretty cheap) can reach sufficient power density when focused to a small area.
All that said, a home experimenter would need some real talent and persistence to do what you want to do. You might do well to investigate photorefractive materials and phase conjugation, which can be used to implement optical transistors and all types of Boolean logic gates.