Am I permitted to perform Hajj on behalf of my father in Egypt, given that I have performed Hajj for myself three times, and he has not performed Hajj due to lack of financial means, even though he is healthy and well?

If your father is in good health but financially unable to perform Hajj, then Hajj is not obligatory for him, as Allah Almighty says: (And Hajj (pilgrimage to Makkah) to the House (Kaaba) is a duty owed to Allah by mankind, those who are able to find a way there). It is not permissible for anyone to perform Hajj on his behalf, but you may assist him financially so that he can perform Hajj himself.