Is it permissible to abandon the husband in bed for fear of diseases, if the husband does not pray, neglects his marital and parental duties, lies, and has an illicit relationship with another woman?

A wife must obey her husband if he calls her to bed, and her refusal without a legitimate excuse is a sin. The fact that the husband has an illicit relationship does not justify her refusal, unless it is proven that he is afflicted with an infectious or repulsive disease.

As for your remaining married to this man despite his abandonment of prayer and his forbidden relationship with another woman, both are grave evils. You must advise him and explain the seriousness of his actions, especially abandoning prayer. If he repents, then praise be to Allah. But if he persists in his misguidance, there is no good for you in remaining married to him, so seek a divorce, even if it requires a payment from you to him.