Your lawyer always works for you. You pay them with the company's money. Which is also generally investor money. But that's ok; your lawyer will be very clear that they work for the company. (Which, it important to note, is different than working for the founders.)
Here, VCs require you to pay their legal expenses for doing the deal. So when the deal closes, they send you a bill for their lawyer. The VC's lawyer definitely knows who they are working for: the VC.
One of the problems with this, besides the you-must-be-fucking-kidding-me factor, is that the VC's lawyer has no incentive to keep things quick. The VC has a very slight incentive to speed things along. But if it's coming directly out of the VC's books, then hopefully they'll keep a tighter reign on all the last-minute stuff that somehow hasn't been made standard and turns what you'd think would be an easy thing into a $25k bill.