Hi Maren,
Did you receive any error messages when trying to add contacts on this specific account?
Can you search any contacts with Lync application on this account?
Since you are able to add contacts if sign in with a different account, it indicates this issue is a separate account related problem. In this situation, as the first troubleshooting step I suggest you create a new Office 365 account and assign the Lync Online license, check to see if the issue occurs on this new-created account.
Thanks,
Bourne Zhang