This request sounds suspiciously like "train your replacement so I don't have to pay anyone"
Right.
It's probably part of an alchemist's training to be self-sufficient and to understand how to gather materials so that even if they have no funds they can do their job and start earning money. So I do think part of her motivation is for Lumia to learn from observing Shuu.
With that said, it's probably more convenient for alchemist to have adventurers gather the materials and to spend their time doing the processing, as that's the main purpose of their skills and how they add value to the end product so obviously they would want to spend most of their time doing that rather than gathering materials, so I don't think the end goal is to replace Shuu.
She might also be curious about how a fledgling adventurer is delivering materials in such impressive conditions and wants to know more about him to see what else she might be able to request from him. So Lumia might actually be tagging along with the express purpose of observing Shuu and assessing his potential rather than studying his techniques. He only just became an E rank adventurer after all, but if he can raise his ranks and perhaps gather even rarer materials it'll be worth it to develop a good relation with him and there's really no better way to do that than to spend time with him.
So yeah, I'd say when she joked about asking to take care of Lumia, and then stated she actually wanted her to accompany him while gathering four materials, she might really be hoping that he will take care of Lumia on a long term basis, so this request might actually be a "job interview for a loooong term contract".
In any case, since he's got a special bag and specialised skills to detect materials it'll be difficult for anyone to do what he does. Also, Lumia is definitely going to notice that he has lots of powerful magic if he ever gets careless again and encounters a powerful monster.
Anyway, chapter was too short. Need more.