I have a bright green accent wall with dark brown on the rest of the walls. I plan on carpeting in a dark brown, although I would prefer dark brown hard wood flooring with a bright green and brown area rug.
My niece recently inherited her big brother's room when he moved out that had gray almost black carpet. She painted the walls a bright, funky green and it looks great together. It was quite an accident as she planned to replace the carpet, but it looks so good she kept it. GL
The standard principle is to use a main color such as your lime green, a second color which is close such as a subtler darker gray-green, and then a totally different small-amount accent color, which in this case would be persimmon. For all this I would use a straw or cream or tan color area rug on a hardwood floor (not wall-to-wall).
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