Do you need a main breaker on a sub panel?

Inside the same building, no. A sub panel does not need its own main breaker as long as the feeder supplying it is protected by an overcurrent device at its source, sized not greater than the panel rating, per NEC 408.36. The breaker in the main panel that feeds the sub is the protection, so a main lug only panel is fine.

Same building: main lug is legal

The feeder breaker upstream does two jobs: it protects the feeder conductors per 240.21 and it serves as the required overcurrent protection for the sub panel busbar. If you feed a 100 amp rated sub panel with a 60 amp breaker in the main, that is compliant. What you cannot do is protect a panel at more than its rating, so no 125 amp feeder breaker onto a 100 amp bus.

Detached buildings change the answer

Run that feeder to a garage, shop, or shed and NEC 225.31 and 225.32 require a disconnecting means at the detached structure, installed at a readily accessible location nearest the point of entrance of the conductors. A main breaker in the sub panel is the cleanest way to satisfy it. 225.33 lets you use up to six switches or breakers as the disconnect instead, but one main breaker avoids the six-handle count argument entirely and most inspectors expect it.

Do not forget the rest of the detached building package

Four wires out: separate neutral and equipment ground in the feeder, with the neutral floating in the sub panel and the ground bar bonded to the can. The neutral-to-ground bond happens only at the service. The detached building also needs its own grounding electrode system per 250.32, so plan on ground rods at the garage unless a concrete-encased electrode exists. Skipping the electrodes is one of the most common red tags on detached sub panels.

Field notes

Buying a main breaker panel for a same-building sub is still often worth it: it gives you a local kill switch for service work, and the marginal cost is small. Just remember the main breaker in a sub panel is a disconnect, not overcurrent protection for the bus; the feeder breaker still has to be sized to the bus rating or less.