While playing an equipment deck, I have been granting double strike to Lightning, Army of One and I've found that when her power is 1 less than enough to assign lethal damage for the first strike damage this leaves the blocker with 1 effective toughness for the second strike, but instead of dealing 1 to the blocker and the rest to the defending player, the normal combat damage is fully prevented. The blocking creature survives, and no trample damage is dealt to the defending player. Both times I've seen it happen were when I was being blocked by Valgavoth, Terror Eater and Lightning had 8 power when attacking.
Platform: Steam PC