If LM was intentionally unhoused, he had nowhere to store what he carried on his backpack. I think he intended to be transient and mobile, and I wouldn't be sueprised to learn that he was homing in on his next target.
Guessing he felt quite invisible at a random McDonald's in Any City, USA.
And who would expect an alleged murderer to be in public, so nonchalant? No one. It had to feel surreal to the witness who thought it was him. Top to bottom, I think LE approached him casually because no one expected it to be him actually.
I wonder who was next in his list. For me, that's why he had his backpack, filled as it was, with him. He was on a mission, his.
JMO