The fic is a redemption fic for Loki and I think it begins with Thor dragging Loki back to Midgard to repair the damages he did during the invasion.
The fic is not Lodestar however, even though it sounds like it and I'm pretty sure this is a non pairing GEN story.
Loki has his magic bound and can only use it to aid people so the first thing on his agenda was to make a point and go up to a collapsed/damaged school and make a completely new one. Then my memory goes a bit fuzzy and I think Thor takes him to a hospital to heal the survivors of the invasion. People with cut limbs, burns, who are dead, are then healed by Loki or resurrected? He gets ambushed by some people on the way out and tells them he can only resurrect recent deceased people. There was also a part where he heals this little girl and her parents are super grateful only for him to tell them that she might have a tumour or something. Loki uses the emotions like hate fear happiness and turns it into energy for his spells, he chooses to use fear or hate instead of happiness and it leaves him more exhausted.
(I think this might be a different fic but I also remember at a certain point that there was a battle and he drew runes around some civilians to erect a shield and he noticed there were two mortal sisters. The younger one was crying so he made her a flower and the older sister was suspicious of him. He asked the older girl if she was a virgin because the blood of a virgin can make a powerful shield. She thought he was a perv at first but after he explained it was for the shield she let him use her blood. As he was drawing in the last runes some assholes barge in and try to rob the civilians and they saw Loki and were like "Hey its that one supervillain guy who invaded earth right?" to which Loki basically replied with "Yeah I'm that supervillain conquerer guy that tried to make you puny humans kneel, go and rob these civilians for all i care" and acts like he doesnt care. The assholes then slapped the lil sister after taking her possessions and then tried to molest/rape the older sister. Key word being tried since Loki then stuck a knife in their backs and crushed the other dudes balls. The sisters started crying and hugging the blood soaked Loki and Loki glares at the other staring civies and the one kid with a camera till they look away.
FOUND by columbialion14 : The Poetic Edda (was almost entirely wrong) by PhoenixVictoria.
(Sorry for any tagging errors on my part, I haven't been on live journal in years.)