No. And if somehow by divine revelation it comes up in an interview, through gritted teeth and probably shedding a tear, you smile widely and say "No, I absolutely loved my time at X lab. I am so grateful to have worked under the tutelage of Dr. X, who graciously offered knowledge and insight into the inner workings of X project. I learned X, Y, Z."
I don't know this person or your situation and won't pretend to know. What I do know is that there is a difference between pain and suffering. By not taking the credit for the work you did do under this individual, they push you past pain and into suffering by making that time you spent with them a waste (at least, academically and in the eyes of evaluators).
Don't let them win. The way you take back control over your narrative is choosing to focus on the positive. If you want to explain what you learned about yourself within conflict, only do so with critical distance, i.e., be general—don't air out your dirty laundry.
These are not academic court proceedings and treating the application like it is will confuse evaluators. Think about it like a job application (ultimately, it sort of is): would you want your future boss to know you left your last job on awful terms with a supervisor? It inspires all kinds of questions you may not be prepared to field, none of which have possible answers that could make you look good.
Disclaimer: I'm an applicant like you. Just my 2c, take it or leave it. I chose not to discuss conflicts in my application: I had a lot of positive things to say about my work and felt highlighting conflict was a poor use of space, but that's just me.
