I've never seen the Japanese Radical Rescue box until I looked it up just now. That certainly looks more anime-style and not likely drawn by Lavigne/Brown. (I got confused earlier; I always thought Brown did the pencils while Lavigne did the inks but it's the other way around. So putting Lavigne's name first makes more sense, and it's also how the duo is referred online.)
Looking up Lavigne/Brown drawings online can be a confusing experience because over the years they drew the Turtles quite differently, but sometime between the early and mid '90s they fell into a style that was pretty consistent. They're still doing drawings even now for conventions, including re-inking old sketches, and the style is completely different now than it used to be.
The Japanese Turtles in Time is definitely them. Well, I guess I don't know authoritatively, but it matches other work they did at the time and the basic drawing existed before the game. I'm not sure if they drew the background art for the box but I believe the drawing was used on merchandise prior to Turtles in Time.