Lydia's likely sticking with him, especially if he finds her in the dark and makes sure she's armed. MOstly because she and Kenshin work VERY well together, and she's perceptive.

Her jobs, though not active at the moment, would allow her some measure of keeping up with him--but she's pretty quick on her own. (Girl travels around a lot, and does a lot of running from danger. It's almost as bad as a Whovian companion.)