As others have said, you have questions of legality and of the actual value of the list.
Second, the value of the list. Typically, Web design businesses are relationship-based businesses: the designer and their client build trust and work together to create the end product. Repeat purchases come because the client trusts the designer enough to return to them. Buying the customer list doesn't buy any of that trust -- all it is is a list of contact information for people who were once, and still may be, in a decision-making position for a Web design purchase at various companies. That's not worth a ton, if you ask me, since you're not far beyond what you could get by just looking at those companies' Web sites right now.
What you need to do is somehow buy that trust. Instead of paying a flat cash fee, why not ask the principals of the other design group to personally connect you to the clients of their choice, offering them a generous commission to do so. They can hold your hand through the initial contact and make sure that you get things started with the potential client right. You may have to pay a flat fee per name for this service as well, but it's the most likely arrangement to turn out well.