What do you mean 'no Edit button on the Apple ID option' ?
If you've updated the primary email address on the account (and that account downloaded that app from the store), then if the old email address shows in Settings > iTunes & App Store (and in the app) then tap on the old id in Settings > iTunes & App Store and tap 'sign out' on the popup and then log back in with the updated version of the account so as to 'refresh' the account on it.
If the app was downloaded by a different account then you will need to log in with that account, apps are tied to the account that downloaded them