Lyle was speeding through the city as he chased after the killer who was moving with great speed as he was a high-grade Silver Knight. Still, if Lyle wanted to, he could have easily overtaken him as not only was he at the very peak of the realm, but he was also in a boosted state as it was nighttime.
Lyle wanted to wait, he wanted to make the person that stole the merchant's body believe that he is faster and slightly stronger than he was so that the latter would go wherever his hiding place was and find out more about him and why he was killing all the people.
Of course, there was another reason why Lyle was following him as he was certain that this person was the murderer that the entire city was looking for. Upon killing the merchant, Lyle was certain that the military would do their best to conceal the news, so he didn't think the person would find out so quickly and even steal the body.