Run the line?

[Nevadaref]

The comment for the rule change 7-5-7 in the 2001-2002 Rules Book was: "THROW-IN PROVISION AFTER A SCORE (7-5-7): To prohibit the team that just scored from gaining an advantage, this change permits a team to run the end line on a throw-in when either a foul or violation is committed by the scoring team immediately following a made basket or on the ensuing throw-in. This change only applies when the spot for the throw-in would be at the end line."

This means that the foul or violation occurs while the ball is dead after the goal or DURING the throw-in which follows. Note that violating as the ball is touched on the throw-in, such as a kick, is considered to be during the throw-in.
In the case of violating on the second free-throw attempt, the team is not violating during a dead ball or during the throw-in, so this rule doesn't apply.
And as rainmaker said, this also applies after an awarded goal.