My newly bought lightening cable is not working.

If you purchased it at either an Apple Store or an Apple Authorized Reseller:

• You had 14 days, from the purchase date, to return it for either a full refund or a replacement.
• Past 14 days, you would need to have an Apple Technician inspect the cable to determine if the issue was a manufacturing defect or not.
  • If it is, you could get a replacement for free.
  • If it is not, then you would have to purchase a replacement at your cost.

If you purchased it from another third-party seller, you will need to negotiate with them on their warranty policy for replacements.

If you purchased it at the Apple Store, check with the store you purchased it at. If not purchased at an Apple Store, where did you purchase it?

yes warranties are not something shops decide it's the law of the country you live in that set that

Warranty - Wikipedia

if it's an apple product read

Legal - Hardware Warranties - Apple

Not sure why you would think that I'm wrong. It appears that this "service center" is NOT an authorized Apple one ... and thus, you need to deal with this center for repairs/replacements and/or warranty claims.