O365 Distribution lists

It depends on where the Distribution lists reside if it's on-premises managed distribution list you can modify the DL as you usually do and then the changes will be synced up, like new members, to the cloud, assuming you have Azure AD Connect in place.  You can also https://support.office.com/en-gb/article/Create-distribution-lists-in-the-Office-365-admin-center-b1ffe755-59e5-4369-826d-825f145a8400 and manage, cloud based, distribution lists directly in Office 365.

Alternatively, recreating the on-premise based Distribution lists in the cloud has some benefits and then they can easily be https://support.office.com/en-gb/article/Upgrade-distribution-lists-to-Office-365-Groups-in-Outlook-787d7a75-e201-46f3-a242-f698162ff09f at a later point if they https://support.office.com/en-gb/article/Upgrade-distribution-lists-to-Office-365-Groups-in-Outlook-787d7a75-e201-46f3-a242-f698162ff09f#bkmk_which.  There are some scripts that can http://blogs.perficient.com/microsoft/2016/05/office-365-script-to-move-mail-distribution-groups-to-the-cloud/.