Your landing-page-domain-name should be used strategically. People will decide whether or not to click on your link or PPC ad based on your domain name.
Just like the landing-page-file-name, your domain name must match the topic of your landing page. People are very sensitive about wasting their time on irrelevant searches so they look to the domain name and file name, in addition to the title and description before they click on the link.
Some people think they can trick people into going to their site by using a domain name and file name that is not directly related to the keyword being searched. Well, they may be successful in getting people to that page, but they certainly won't sell much.
The reason for this is simple, you want people who are actively interested in buying what you are selling. Trying to sell to an un-targeted visitor is very hit and miss. Mostly it is a miss.
If you are paying for each click in PPC advertising why would you want to pay for anything other than a "hot prospect"?
This is a copywriter's ideal scenario. Now you have the right person listening to your spiel. All you have to do now is show that you can deliver what your prospect is looking for, at the best possible price and you will have a sale.
The landing-page-domain-name is an essential copywriting tool that adds credibility to your message. You can use a related domain name and still get good results, but you will get the best visitor-to-sale conversion if the keyword typed in by the searcher matches your landing-page-domain-name.
Just as you need to create a separate landing page for every keyword group in your PPC advertising, you need to register a separate domain name also.
The cost of registering domain names is very inexpensive these days. Here is a good place to get good web-hosting as well an inexpensive domain names.