Personally, I’ve never been able to get sub 10% bodyfat without protein making up at least 40% of my total caloric intake. My last cut it was even up to 60% by the very tail end, but I hit about 6%. Idk how lean you’re trying to get. I’ve never had any issues maintaining muscle with this approach.
Also, I’m not saying you can’t keep cutting training 3x/week, but it will be a challenge. I’d recommend hitting the gym 5-6x a week.
I made this post awhile back. Worth a look for some more in depth ideas: When Your Cut Stalls