Lily knew she wasn't meant to be out after dark, and really, she hadn't meant to be. It was just her knack for losing track of time. She'd already used her mirror to alert Sirius to the fact she was on her way home. She could have apparated, she knew, but she still didn't trust it completely in the confines of this cage. For all she knew, the cage would spontaneously shrink while she was mid-movement and she'd get stuck in some sort of limbo.
It was highly unlikely, she knew, but she found it just as easy to walk and not deal with the worries of it.
When she passed an alley, she paused and cocked her head curiously. Was that --? She frowned a little as she saw what she was fairly certain was a witch with her wand out. "Excuse me," she said gently as she started down the alley. "Have you just arrived?" She asked politely. It was possible the woman had been here a bit and had just ducked into the alley to hide her wand from the Muggles. If that was the case, then Lily would excuse herself and be on her way.
But if the woman was newly arrived ... well, she'd want to help her out.