Is it ok for Christian men to go out with women that are not their wife, to lunch, dinner or other entertainment?
I'd give that a qualified "No".
Obviously, if the "woman" is his sister, mother, daughter, or other close relative, then it's fine. Where a relationship would be unethical, say with his lawyer, it
might be okay to have lunch while discussing a case, but nothing more intimate. In such a situation, both should be considering the risk and proceeding accordingly.
Most other situations would be questionable at best and downright dumb at worst.