Can the visiting team change their starting pitcher once the line ups are given to the umpires and the game begins? Example- Joe Strikeout is the starting pitcher on the line up card. The visitors score 8 runs in the top of the 1st and they trot out Bill Not SO Much instead of Joe Strikeout. Legal substitution?
This is not legal. According to rule 5.10(f) of the 2016 MLB Rulebook, the starting pitcher, as listed on the lineup given to the umpire, must pitch to the first batter he faces (unless said pitcher is incapacitated for whatever reason). That batter must be put out or reach base before the starting pitcher can be replaced. In your scenario, the visitor's starting pitcher has yet to face any batter from the home team, and thus, cannot be replaced until he has faced the first batter from the home team.
The pitcher named in the batting order handed the umpire-in-chief, as provided in Rules 4.02(a) and 4.02(b), shall pitch to the first batter or any substitute batter until such batter is put out or reaches first base, unless the pitcher sustains injury or illness which, in the judgment of the umpire-in-chief, incapacitates him from pitching.