See:
http://www.hp.com/rnd/support/warranty/index.htmNote the little "1" next to the Lifetime. Down at the bottom we see:
1 for as long as you own the product.
So my interpretation would be: There is no lifetime warranty on used equipment. This interpretation is strengthened by the statement further down on the same page:
"When you call, please have the following information available:
product number (for example, HP J3200A)
serial number (for example, serial number US41400480) or date code (for example, A-3802-D3)
complete description of the product failure
proof of purchase of your product"
Note the last requirement for: proof of purchase. To be 100% positive you would need to call HP and ask them but I think you are out of luck.
Ron