From Grand Canyon Village (South Rim headquarters) to Grand Canyon Lodge (North Rim), you're not just heading east—you're crossing the canyon.
Grand Canyon Lodge sits on the North Rim, ~16 km (10 mi) straight-line north-northeast of Grand Canyon Village (South Rim). But you can't drive there directly.
By road: 345 km (215 mi), 4.5-5 hours.
No bridge spans the Grand Canyon. The Colorado River cuts 1,600m deep. The only crossings: Navajo Bridge (Marble Canyon, 130 km downstream) or Hoover Dam (320 km downstream). Seasonal closure: North Rim open May 15-Oct 15 (snow).
South Kaibab Trail → Bright Angel Trail: 39 km (24 mi), 1,800m descent + 1,400m ascent. 1-2 days. Phantom Ranch at bottom. Permit required. Not a day hike for most.
If it's November-April: North Rim is closed. Grand Canyon Lodge is inaccessible by vehicle. You're not going there.
East? Yes. Direct? No. The canyon decides the route.