I definitely plan on negotiating. I wanted to get thoughts and feedback on what you have seen in the past.
anything more than that is a strict value call on your end. Is getting the exact domain that you want worth the extra thousands and thousands of dollars?
also, it strikes me as odd that you are calling the other person a "seller" when they are offering you a lease on the domain. are you aware that "lease" is just another word for "rent"?
honestly this sounds like a terrible idea that you haven't fully thought through.
IMO, domains are growing less and less important as more people find sites by clicking on links, not by typing in the domain name.
So many successful companies start with getMyApp.com instead of MyApp.com.
That being said, it's not too bad a deal, you are only out $2K if you have a taste and the domain doesn't deliver.
BUT cut out the equity piece. These type of shareholders are at best pure dead weight and at worst a pain in the ass.
One other note, even with a contract, there are ways the seller can screw you (eg. changing their bank acct details & going incommunicado) so if you are leasing make sure the domain is controlled by a neutral 3rd party for the lease term so you are protected if someone with a better offer comes along.
My opinion is that you should save the money, choose a different name (or variation of the name), and put the $2k/month towards something that will provide real value to your startup. There's a ton of one dictionary word domains available if you have a little creativity, and, since you're new, you're presumably not really tied to any one name.