I’m becoming Catholic soon, and to make a long story short I have to hide this fact from a certain person for their own good. Now, I’m going to tell you about a situation that I’m very concerned about. If I were in a situation such as a barbecue around that person, where of course meat is the main dish, and it was a period during lent which I couldn’t eat meat, what would I do?

This person just couldn’t handle the fact that I’m becoming/became a Catholic. He’s VERY prejudice about our faith and sees it as heresy and betrayal of God and everything he stands for. So, if I were in this situation or something similar to it, would it be mortal sin to just eat the meat to prevent an unstoppable drama fest?
The other posters have given you good advice, and BTW, welcome to the Church. I know it is a big step and sounds like you will be the “first” in your family.
There are two issues in your post, as has been brought out. You should be able to do a “work around” during Lenten Fridays and such by just choosing not to eat meat. Unless everyone you know is a committed carnivore, and the only food they serve is meat, you should be okay. People may be Catholic, they may be Vegans, they may be on a diet of some kind. It is no business of anyone else what you eat or why.
However, you can’t “hide” the fact of becoming Catholic from this person forever. If you are uncomfortable with being confronted by him you may want to think of how you can “soften” the blow. Perhaps having someone else tell him. But if you can handle it, the best way is a frontal assault. Just tell him that you have made this decision, and you understand how he feels, but you feel in your heart that you are making the right choice. Then say something like “I hope you can understand and respect my decision.”
Another way to approach it would be to write him a letter so he would have time to read it and “cool down” from his initial reaction. Also lining up support with others in the family or close frends ahead of time could help, since this type of person may not act belligerently if he is “alone” on the issue.
I know someone a little older than you who went through the same decision once, and worried about how his family would react. They were surprisingly understanding and ending up supporting his decision. Your situation may not be that simple, but it is often less “confrontational” than we think it will be.
Finally, I don’t think you are withholding this for the benefit of the other person, but more out of fear about how he will react. It is not easy to take a step like this, when someone close to you is opposed to what you believe. Imagine what it was like for the first disciples, and use their faith and determination to strengthen you.
Good luck, and God Bless.