There were numerous areas inside the facility, but Lyle was unfortunately not able to enter the smaller, more secretive ones since he could see that only those wearing white coats were able to do so. He wanted to grab one and kill him before taking the clothes and disguising himself, but there was actually a much better way to infiltrate the place.
He stalked a group of two white coats who were walking around. He couldn't see the chest that they used to take the bodies, so he wasn't certain that these two guys belonged to those that did such a job, but after seeing a couple of white coats bowing slightly to them in respect, he was able to determine that the two were quite highly ranked.
He continued stalking them, but even after almost 1 hour had passed, he didn't have a chance to go through with his plan as they never entered any area that was empty. He needed them to be all alone in order for his plan to work.