Sigh. Of course that’s true—we know that because that’s what she does.
But neither of those answers can be the whole story.
If “for business purposes,” that makes no sense—if she needs a short-haired, light-haired model “for business purposes,” then why go out of her way to make over a girl with long, dark hair?
I'm just making assumptions based on what've seen so far.
In ch.10 she seems like the strict business type that only cares about Liz because her company is involved with her band. In ch.11 she's the one behind Liz radical makeover, praising her new hairstyle (we didn't know it was a wig) and then choosing a dress for her. Both the hairstyle and the dress don't fit Liz punk/rock public persona, but we can assume there's a valid reason for Sumire (at least from her point of view) to do this and since she's a business woman I guess it probably has something to do with her company sponsoring Liberty.
Sumire is a manipulator who easily swayed Liz just to have some fun in high school and we can assume she's doing the same thing now, she certainly isn't in love with Liz.
If she wants to remake Liz’s image to her own liking, then why have sex with her in her original hair?
First of all, to show the readers that the new hairstyle was just a wig. There're probably better ways to do this, but ok.
Second, maybe to symbolize the contrast between the "new" public image of Liz and her "old" true self? Who knows. We can only wait for the next chapter and hope it will shed some light on Sumire's plan.