Is a person's work considered unlawful if they obtained it through lying and falsifying facts in the interview, which may deprive another deserving person of the job?

If you were accepted for a job through deceit, you must repent. If you perform your work fully, then the salary is permissible (halal). However, if there is someone more deserving of the position from a waiting list, it is better for you to relinquish it to them, and Allah will compensate you. If that is not the case, then continue your work and perfect it, and repent to Allah for what you have done.