With the Exchange Administrator role you can manage email Distribution Lists through the Office 365 Administrator Portal:

portal.office.com

To find your Distribution Lists, scroll to the bottom of the Office 365 Admin Center menu on the left and select

1) Admin Centers > Exchange :

To edit an existing Distribution List, from the menu on the left in the Exchange Administration Center,  select

2) Recipients

3)  Groups

Select the Distribution List you want to edit then select

4) Pencil icon to edit the selected list

To add a member to the selected list, on the list detail page, select

5) Membership from the menu on the left and then select

6)  the "+" icon to add a member.  

From the select member window,

7) select the member you want to add, then

8) click Add or OK

If the member you want to add is an external address not already listed in the select member window,  add a new mail contact, by starting from the main menu on the left in the Exchange Administration Center,  then select

9) Recipients

10) Contacts

And in the Contacts Window select

11) the "+" icon then

12) Mail Contact to enter the external email address.  Then return to the instructions to Add a Member above  (steps 5 through 8).

To remove a member from a Distribution List, from the menu on the left in the Exchange Administration Center,  select

2) Recipients

3)  Groups

Select the Distribution List you want to edit then select

4) Pencil icon to edit the selected list

For the selected Distribution List, on the menu on the left select

5) Membership

From the select member window,

6) select the member you want to remove, then

7) click "-" icon. The member is removed immediately.

8) Save