the first thing to do is not play Fire Emblem on Lunatic, it's not worth it
I played Awakening on Lunatic once, and while I did beat the whole game including motherfucking Apotheosis, that was enough of Lunatic difficulty to last me a lifetime
and manaketes live a very long time mind you
....
But to give a serious answer: I've never played Fates on anything higher than Hard/Classic, but you'll probably want to make use of Ryoma as much as possible, as he's by far the strongest unit on the map and probably the only one that can engage the enemies solo safely. How you do this, I don't know, but I guess you'd have to see how you can manipulate his and the enemies' movement via Dragon Veins. And don't worry about Ryoma/Sakura/Hinoka getting KO'd, as this does not bar them from joining you later if you choose Birthright or Revelations as your path. Also when you have the units directly under you control attack, it's best to have Kaze go first since Faceless can't counterattack ranged units, so he can shave a few HP off of them and debuff them for Corrin and Rinka.
Other than that, looking up (video) guides may help you.
