Non Competitive Martial Arts and Lazy Eye?

Okay so I have question for people. I have always wanted to take up non competitive martial arts but have very bad lazy eye in one eye with one good eye along with cerebral palsy. So my main concern is not only be would I be able to do martial arts with a lazy eye without glasses of 20/200 and if I can what type of protective eye wear should I use when it comes to protecting my eye. This is something that in recent years has deterred me from starting martial arts but it is a desire that I really want to do it. I will be consulting my optometrist about this but I want to get people's thoughts on this.