To edit a protocol in the Protocol steps overview (see the image below), you need to be an Owner or a User at the project level. To learn more how to manage user roles and permissions watch this video tutorial.
Furthermore, if you want to edit a protocol in the Protocol management (see the image below), you need to be the creator of the protocol.
If a protocol is stored under the Team protocols tab, other team members can create a copy of it, save it with another name and make changes to it.
If a protocol is stored under the My protocols tab, other team members cannot access it. However, the creator of the protocol can convert a private protocol to team protocol and make it accessible to others. In this case, a creator must select the protocol and click the Move to Team protocols button.