What is the ruling on my remaining in my job after I lied to the employer twice regarding work experience and the existence of an Eid bonus at my previous company?

You have committed a great sin with your two lies. The first lie has already been explained. As for the second, it resulted in harm to your employer. It is possible that your employer stipulated a condition for the gift, and you falsely claimed its existence, or that he spent his money because of your news. You must repent. If you claimed the condition, you must inform your employer of the deception. Either he forgives you, or you must return the money to him or appease him. If he did not stipulate a condition, then you must repay what you took from him.