[@Duthguy] You can trade with a hero on your map tile if there are no enemies, so you could give it to Hawkeye Harold. If there are monsters on the map, you must be adjacent to the hero you're giving it to though.

Lucky Dice can redraw any card (monster, loot, scavenge, map, ect) but can't change dice. So you'll have to spend a determination if you want more movement.