If you have the same kind I have, yes, it does come with a lifetime warranty.
The name of mine is "Metal Garden Hose". One problem is that this company requires proof of date of purchase so you probably need your receipt, and they want a check/money order in amount of $10 to cover postage and handling plus you have to pay for shipping it to them. Mine costed $19.95 at Menards so all that shipping and handling would come pretty close to buying a new one. But I see other places this hose costs $40 and if you buy it online it's $50.
(I sure love my Menards store