Is it permissible to perform Dhikr in the heart without uttering it to avoid showing off? And will a person be held accountable for lying when compelled to do so by work circumstances, without intending to harm anyone?

Hypocrisy (Riyaa') is more dangerous than the creeping of an ant, and sincerity (Ikhlas) is a great blessing. Therefore, strive against your soul and do not cease performing acts of obedience. Seek Allah's help and frequently recite the supplication: "O Allah, we seek refuge in You from associating anything with You knowingly." Al-Fudayl ibn 'Iyad said: "Abandoning an action for the sake of people is hypocrisy (riyaa'), and acting for the sake of people is polytheism (shirk). Sincerity (ikhlas) is for Allah to protect you from both of them." If you are unable to repel hypocrisy, then remember Allah in your heart when interacting with people. As for your work with the aforementioned person, it is permissible if it is within lawful limits. There is no harm in concealing the matter. If you are asked about your work, you are not obligated to answer. Try to use allusive speech if you need to, but lying is not permissible.