If your trying to see what routes the A340 operates I’d go onto Flightradar24 and make a filter for A340’s to see what routes they do. Hope I interpreted your inquiry correctly.
Well beside from the ones you’ve mentioned, A340’s are set to replace the A350’s at CLT for Lufthansa’s daily service. This change is set to happen on May 1st.
Home airport of JFK gets the Lufthansa A340-600 still. One of the daily JFK-Frankfurt routes is the A346, along with the JFK-Munich route.
Miami is currently seeing the A343 from Frankfurt daily, too.