How strong a bleach is really the question that matters. It is not generally a good idea to mix a readily flammable product with a strong oxidizer, because then the two chemicals will do what they are expected to do: oxidize and generate heat, leading to flame. The presence of water will inhibit the reaction (the lighter fluid will not readily integrate into the aqueous phase and interact with the hypochlorite, so the interaction will be surface area limited, thus concentration of hypochlorite matters as does the amount of water allowing heat absorption).
Fundamentally, though, the idea of adding a target for oxidation (a volatile organic compound) into the cleaning solution kind of runs counter to the purpose of the oxidizing agent, which is to oxidize stuff on the surface to be cleaned. The oxidant will first oxidize the part that you added to the solution (it is what is most readily available). The bleach will get consumed before it does anything useful on the cleaning side. Not a good move in any way.