The following is all the Fed rules book has to say about the running lane.
JL
RULE 8-4-1
ART. 1 . . . The batter-runner is out when:
g. he runs outside the three-foot running lane (last half of the distance from home plate to first base), while the ball is being fielded or thrown to first base; or
1. This infraction is ignored if it is to avoid a fielder who is attempting to field the batted ball or if the act does not interfere with a fielder or a throw.
2. The batter runner is considered outside the running lane lines if either foot is outside either line.