Maybe you have to invert b and c position ?

I see that the c table appears to be the base table :

WITH CTE_Concat AS (

SELECT c.ListID,t.EntityID, STUFF(

(SELECT '; ' + c.ListName

FROM [server].[xxxxxx_MSCRM].[dbo].[ListMemberBase] b with (nowait)

WHERE b.ListID = c.ListID

FOR XML PATH('')

),1,1,'') AS ConcatValues

FROM [server].[xxxxx_MSCRM].[dbo].ListBase c with (nowait) INNER JOIN [server].[xxxxxx_MSCRM].[dbo].[ListMemberBase] b with (nowait) t ON c.ListID = b.ListID

)

UPDATE a

SET Con_Mailings = z.ConcatValues

FROM [xx_Temp].[dbo].[Lyris_CombinedTest] a INNER JOIN CTE_Concat z ON a.TmpContactID = z.EntityID