What is the ruling regarding a brilliant female engineer's refusal to lie in a job interview about her graduation project and to accept intercession for employment, and what should she do given her fear of remaining unemployed?

There is no objection to seeking a mediator to help secure a job for which a person is qualified, and for which no one else is more deserving; for not all mediations are forbidden. Mediation for employment is permissible if the person is competent and able to perform the work, and this falls under fulfilling a Muslim's need. A Muslim woman should seek out workplaces that are suitable for her and that are not associated with Shariah prohibitions.