If Eid falls on a Friday, the Eid prayer becomes permissible and then gives permission for Jumma'h prayer / Luhar prayer to leave
Fatawa Saylani : If Eid falls on a Friday, the Eid prayer becomes permissible and then gives permission for Jumma'h prayer to leave. If they wish to back to their homes and not to return for the Jumma'h prayer then it is upto them , if thay want to return after leaving , and then come to perform the Jumma'h prayer, it is permissible. Although if they don’t, there is no harm, in-sha’Allah. i.e : meaning leaving the Friday prayer that exempts them from the obligation of performing the Jumma'h prayer. listen the audio
In Sunan Aboo Dawood , and in the Musannaf of ’Abdur-Razzaaq with an authentic chain of narration from Abdullaah Ibn Zubayr that he said:
‘‘Two ’Eeds coincided on the same day and so they were both joined together by making them one. He prayed on the day of Jumu’ah two rak’ahs in the morning and he did not add to them until he prayed the ’Asr Prayer ...’’
Ash-Shawkanee said in Naylul-Awtaar after this narration: ‘‘It is apparent that he did not pray Dhuhr Prayer.’’ It also shows that if for any (permissible) reason, the Jumu’ah Prayer is cancelled it is not obligatory for the person for whom it has be cancelled to pray the Dhuhr Prayer and ’Ataa‘ held this opinion.
As to our knowledge , there is no any narrations available to Pray " Salathul Luhar ", while omitting the Salathul Jummah expcept the assumptions and analogy. The Base in the worship is that you have to act as to the text and not of anything else and as well no analogy should be used in the worship matters.