Unless "lifetime" is clearly defined, a "lifetime" warranty doesn't necessarily mean much. What or whose "lifetime" is the deciding factor? Many people assume it means their lifetime, but that is rarely the case. Usually it means the expected lifetime of the product, and guess who determines what that expected lifetime is. I rarely buy anything based on the claimed length of the warranty, but to each his own.
Anyway, if you buy a product with a one or two or umpteen year warranty, and the product has to be replaced under that warranty, usual practice is that the product you receive under warranty does not come with it's own warranty starting at zero again, but just the remaining portion of the original warranty. If otherwise, it must be disclosed to the customer up front.
Jerry