Actually, that is more like a band/drum brake than a roller brake, although Dia Compe does call it that. Roller brakes generally have a port for some sort of special grease (the
Shimano Nexus Roller brake is a classic example) which improves their braking power. You do not put any sort of lube on a band/drum brake. In
@mizuto's 2nd and 5th images, you can see the spring loaded tensioner at the bottom of the band. This is usually adjusted by loosening the bolt locking in the brake cable and squeezing the spring a little tighter as you pull on the cable, then re-tightening the bolt.
Perhaps the bike shop will show you this adjustment; band brakes are notorious for loosening more quickly than a typical set of V-brakes so it's good to be able to do at home. Good to get a thorough tune-up anyway if that hasn't been done in a while!