Lily is a workaholic that she work 10 hours every day This sentence is just plain wrong! Lily is a workaholic. She works 10 hours a day. I must point out though, that someone who works 10 hours a day is NOT a workaholic. Workaholics work and do nothing else. Probably 16 hours a day or more.

I think I discovered the site where you found this sentence. The writer clearly made a mistake: the only correct way is "she works".

As you say & 雲小泉 said in a round about way. Yes. "She works" is correct for the third person singular.

there is another expression : she works around the clock