Centurylink does give you the option to either buy a DSL modem through them or Lease a Modem through them.
I would recommend going for the option of buying the DSL Modem whether through Centurylink or in a store or online instead of leasing the Modem because when you lease the modem you'll be paying more money than the modem is worth and never own it.
You can find a list of compatible DSL modems through Centurylinks website.
https://www.centurylink.com/home/help/internet/modems-and-routers/what-modems-are-compatible-with-centurylink.html
You can go to that link and see a list of compatible DSL modems that work with Centurylink DSL or you can just buy a DSL modem from Centurylink so you know it's 100% compatible.