Since the first expert assisting you has asked for a different perspective, I will be assisting you.
I believe what you will want to do is obtain the domain name from ICANN, the Internet Corporation for Assigned Names and Numbers. They control all internet names, worldwide.
Here is a link to their Uniform Domain-Name Dispute-Resolution Policy page http://www.icann.org/en/udrp/udrp.htm. You will probably need to contact ICANN and find out what procedures they want you to follow for you to execute on your lien/writ; I don't believe your exact situation is outlined in their procedures.
As far as obtaining the actual html or other coding for the website, there is a good possibility that the LLC doesn't actually own it; check the bottom of the website and see if someone owns the coding. That's not the same as the LLC owning the copyright. In order to obtain the copyright, you'll need a court order assigning that to you. That is equitable relief that a small claims court cannot order.
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