Apply penalties based on plausibility
No lie is perfect, especially in 5e. So start tracking the flaws and applying the penalties appropriately. She shouldn't have an easy time convincing people that she's a God, for instance.
Apply penalties based on reputation
She lies a lot. That means she's left a wake of people who believes she's a liar, because they fact-checked her and discovered she was lying, eventually. The more her reputation as a liar grows, the more penalties she gets.
Write plot hooks she wouldn't want to lie to avoid
If she's lying to avoid plots, this is at least likely and partially because those plots don't interest her character. Adding plot hooks that DO interest her character will hook her interest, making her chase your hook, rather than have you chasing her with hooks.
Write plot hooks that anticipate her lying
This can be done several ways, such as with General Tarquinn's book of procedures in OotS, or via meta-gaming her typical type of lies and building a story that makes lying that way catch her on the plot hook. Regardless, you should be careful about doing this too much, as opposed to other options I've specified, as meta-gamey solutions feel worse than in-game solutions.
I say to your players, something else is the way to go. Fake it til you make it. Give 'em the old razzle dazzle. Sell the sizzle.
You can't speak orcish, but maybe you can fake it with the best of 'em. Whatever the orcs say, nod, shrug, moan, make a vaguely orcish grunt, point to your mouth and move on. Or maybe when an orc says something to you, nod, try to make a sound that sounds like a sound the orc just made, and keep moving.
Some props might help. Wrap a bloody bandage around your lower face, and fake an orc with a ogre-size toothache. Maybe some real orc blood will help sell the smell. Maybe drag a "dead" halfling along like you're taking the body to the boss.
A little charisma and maybe some proficiency in performance and deception and some luck is your best bet. Any other spells you got, use 'em -- suggestion, charm person, friends, enhance ability, could all be useful.
A distraction might help. Illusory elves attacking on the other side of camp maybe. Elves, man, orcs hate 'em. Or maybe an ally lobbing a fire arrow into the other side of camp might cause a distraction. Setting fire to the tents is always an option worth considering.
And when the jig is up, and they're getting wiggy on you, you can point in the distance, wide-eyed, make some orcish grunts, and heel-and-toe it out the door. Haste might be helpful.
Best Answer
A missing wing is not easily replaced at lower levels.
You’re right, magic can fix anything, but at lower levels limbs are not so easily regrown.
To regrow a limb you’d need access to the Regenerate spell:
However, this is a 7th level spell. Your PC’s won’t get those until level 13.
Assuming you don’t want your player to wait quite that long to be able to fly, you can insert a 13th level NPC spellcaster into your narrative who wants the party to do them a favour, or let them find a scroll of Regeneration, at an appropriate point.
But is your player going to be happy with this?
Have you discussed with them the idea of taking their ability to fly away at lower levels? How do they feel about this?
Is flight their main reason to consider playing an Aarakocra? If so, then taking away that ability initially may mean they'd rather play something else - with all their racial benefits intact.
Before following this strategy I'd advise checking that your player is on board.
N.B I've assumed in this answer, that in your gameworld an Aarakocra's wings and arms are separate limbs, which is inkeeping with offical 5e depictions but varies somewhat with lore from previous editions. Losing effectively a whole arm (as well as a wing) would have very debilitating implications for combat - ability to use shields, wield 2h weapons etc.