Are the father's earnings considered lawful or unlawful if he concealed his heart condition from his government employer in Saudi Arabia, fearing dismissal, knowing that he needs to save money for a future project, and is the money he sends to his family considered lawful?

The money your father earns from his work is lawful (halal) as long as he performs the duties required of him. His illness does not affect the permissibility of his work unless it prevents him from performing his professional duties. The evaluation of his performance rests with the entity he works for.