You could always get a cheap plastic basin just for washing your lingerie. I did that recently (I think the item I bought was meant for pets) and now I don’t have to worry about the sink being spotless anymore.
You could also divide your lingerie into sink-sized piles or machine wash some of your less delicate pieces (like your cotton knickers or what have you) to make more sink space for your more delicates.
Really, there are a lot of options (aside from a wiping out the sink with one of those Clorox bleach wipes…my personal favorite) if you’re worried about crud winding up on your lingerie. :-D