Hi,
Well, you mentioned some of the members who have rights to edit the site is from DL. Then inviting the distribution list into Sharepoint team, setting the corresponding rights, regarding them as the Sharepoint team member, so the authentication mechanism which you use is also suitable for those members from DL.
Thanks.
Sincerely,
Michael Jin.
Microsoft Online Community Support
?Please remember to click ?Mark as Answer? on the post that helps you, and to click ?Unmark as Answer? if a marked post does not actually answer your question. This can be beneficial to other community members reading the thread. ?