I have a user who is an exchange admin. Odd, I know. But can she go into outlook and make changes to the company's distribution lists just in outlook365 somehow? I just want her to have the ability to add and remove members
I remember at another company if a person was a manager of a group they could just navigate to it in the GAL and "modify" members. I want her to have this access
If the distribution groups are sync'ing from local AD to O365 (AAD Connect), the membership can be managed only from on-premise AD/Exchange servers. If the distribution groups are created directly on O365, your Exchange admin can manage its membership from Exchange Admin Center. If she's added as an owner of the DL (which she can do herself from the EAC), then she'll be able to manage its membership from Outlook as well.