what is the rule on how far a lineman can go down field on a middle screen.

There is no restriction on ineligibles going downfield IF the pass does not cross the line of scrimmage. On a properly executed middle screen, it won't.

But I'd guess your question is prompted by a situation that occured in one of your games. My guess is that a middle screen was attempted but the receiver missed the ball, or it was overthrown, and the pass crossed the neutral zone while the blockers were downfield. That would be a foul for ineligibles downfield, or maybe even offensive pass interference.

So the simple answer to your question is - two yards, the width of the expanded neutral zone.

We had this in a playoff game last year. During the playoffs, the NCHSAA assigns officials to work teams that they normally don't work during the regular season. Home team runs a middle screen. The back is two yards beyond the LOS and the lineman are 5 to 7 yards downfield when the catch is made. I drop my flag. They couldn't believe it! "We've been doing that all year and no one has called it."

I wish I had $10 for everytime I've heard that! :D