Contrary to some of the comments; the cover is only there to protect the hose reinforcement. Wire braid under the hose cover very quickly rusts and fails if exposed. However, a hydraulic hose with no cover at all will hold pressure, as long as the reinforcement is not compromised. If you cannot see the wire under that scuffing on the original hose, it has not compromised the hose in any way other than cosmetic. The layline tape has come loose but that is only there to show the hose rating and size info. If the reinforcement wire is not visible, you can wrap the hose in heavy duty tape, like Gorilla Tape, and it will not compromise the hose pressure capability at all. Your choice how much you want to spend.
I've worked as a hydraulic hose engineer for Parker Hannfin for 25 years. I would not buy that same hose from the lift manufacturer, simply because any Parker, Aeroquip, Gates, Weatherhead, AlfaGomma, Ryco and other brand hoses are far better quality than Xufeng (made in China) and is honestly some of the cheapest built hose around. Parker makes hose in China also, in Parker facilities and made to Parker standards. For me, only Parker hose because I know it works in all applications I've used on mobile equipment from skid steers to underground coal mining, and everything else.
Could probably find a suitable hose match at any Tractor Supply store, just get one close to the same length of the original, with the same end connections. Since it is a motorcycle lift, speed is not the issue, so you could match that hose size, or even go slightly smaller and not affect the lift action much at all.
That info on the hose designates it a 2SN DIN spec hose, 8N means it is 8mm metric ID, or equal to 5/16 inch ID hose. DIN is the German hose spec, buts nothing about where the hose was built. The 2SN DIN spec in that size hose is working pressure rated to 3,125 psi. But I really doubt your lift is anywhere that pressure range. Many manufacturers over spec the hose if they can get it cheap enough. Most likely the system pressure is more like 1500 psi . The owners manual should tell your the rated pressure of the system. IF indeed the system is rated to 3,125 psi, then you could use any common 1/4 hose pressure rated as a SAE 100R2 hose, in 1/4" size it will be rated higher than your original hose. Or use a SAE 100R17 hose in 1/4" size it will be rated to 3,000 psi. If you really want to stay with the 5/16" ID size, either 100R2 or 100R17 hose will suit.
A lift, like a jack, is a very low duty cycle application, and does not require a 2SN rating. All SAE hoses are duty rated 4:1 for the working pressure. So again, either 100R2 or 100R17 hose will more than meet the duty cycle need. Many NAPA stores, any Parker Store, Gates distributor, Weatherhead distributor, Fastenal, can make you a matching hose assembly. But I doubt Fastenal uses any common brand name hose. But again, I really doubt you need a 2SN DIN spec 8DN hose, and you'll pay extra for that if you get the same spec.
If you want, PM me pictures of the hose end connections and I can tell you exactly the components needed to make a new hose assembly.
