Is it unethical if I did not inform the current lab I am in that I am looking for another position? I would like to know whether I should inform the current lab I am applying for other positions. I feel guilty as someone told me it is unethical what I am doing to hide it from the current employer.

I don't feel comfortable with this current lab and I cannot imagine myself in it for many years, but I cannot inform as the PI here is a bully and not compassionate person at all. Yet, I don't have something in my hand, but I am struggling whether I have to be honest or hide it.

The question is: Is it unethical in academia to hide that I am considering applying for another position while I am currently in?
Generally speaking, no, you can seek other employment at any time without ethical constraint. This is especially true if the work environment is abusive in any way. 

There is one consideration, however, that you should keep in mind. If other people depend on your work, you need to do what you can so that you don't unnecessarily disadvantage them. So, you may have an obligation to complete joint work before you actually leave, or see that it is put into a proper state. But you don't have to do that first.