I suspect you, and your director, want the walk through the alley to be somewhat disturbing, frightening, or foreboding. There may be creative ways of enhancing the scene and at the same time compensating for the lack of lighting instruments. Not having read your script, it's impossible to say, but I would consider ideas that would not only compensate for your lack of instruments, but could strengthen the scene. Figuring out how to do this is interesting. You might put a burning trash container in the alley. You wouldn't need to explain why it was there. It could just be this strange element that the character encounters and passes by. Another idea might be to to put a couple of strange kids with flashlights on the roofs that border the alley. The kids could flick on and off their lights toward the pedestrian as he walks through the alley. You wouldn't have to see the kids, although you might hear them running along the roof. These elements could add a lot of tension to your scene. Again, they wouldn't even need to be explained. They could just exist as part of the character's passage through the alley. Together with sound, they might add significance to the alley while at the same time providing a way of using fewer lighting instruments. Obviously, the best solution is the one that contributes to telling the story in the most effective way. Working within budgetary limitations can create interesting situations. I recall hearing about a David Lynch film where a sudden rain shower threatened to shut down production for the several hours. A parking lot that had been shot as being dry, was suddenly drenched. Not having time, or money, to wait, or reshoot, Lynch solved the problem by having a couple of extras grab water hoses and pretend to have a water fight in the parking lot. It was just enough to explain why the pavement was suddenly wet. It's kind of a dorky solution, but also kind of strange, and, well, very David Lynch.