How can an employee who cursed her colleague with the word "dog" and then lied, denying it, repent, knowing that her colleague used to oppress her and harbor enmity towards her, and she fears that her refusal to reinstate him to work might be a sin?

If your lie was not the cause of the employee's dismissal, then we hope there is no accountability upon you, and you must repent from lying and seek forgiveness from the employee for calling him a "dog." However, if your lie was the cause of his dismissal, then you must appease him and clarify the truth to the officials. We advise you to seek employment in a non-mixed environment if you are not compelled otherwise.