Yes you can.
The player having many options to trivialize Awakening's Lunatic and Lunatic+ difficulty, including grinding, is what makes it imbalanced. FE12 is nowhere near as RNG heavy as the first couple chapters of Lunatic+. Yes your roster choices are limited, the balance comes in the fact that you can't choose some massively OP character to solo the game with, unlike Awakening.
Sorry on that Mage stuff, not Lunatic, but Lunatic Reverse.
And in my personal opinion, you are even more at a complete mercy of the RNG in FE12 than you are in FE13. If the RNG in FE12 screw folks like the MU, Caetra, or Marth badly, then you are pretty much screwed with *no chance* to make it right, unlike in the FE13 where you can grind to compensate. Hell, a lot of people are known to completely abuse the resetting feature for that game if the MU doesn't get level up like +1 speed during the early levels on FE12, and specific MU configurations *guarantee* that you will *not* be able to complete the early levels of that game in hardest difficulty, unlike in FE13 where the players can have a bit more freedom in this regard.
An analogue: consider Lunatic/Lunatic+ in FE13 as if you are wielding a sword and the computer wielding a tank on a playing field. You are horribly outmatched at the beginning. In FE13 at the very least you can train until you can bring a tank too on the field so that you and the computer can stand in an even ground with nothing but tactics and strategies to secure victory. In FE12, if RNG screws you bad then that sword is all you have for the rest of the game while the game throws enemies upon enemies wielding tanks at you. In that way, FE12 is much, much more reliant of RNG than FE13 ever will.
Bonus: in FE12 you are pretty much *required* to train specific characters to prepare for the final battle if you want to rescue a group of characters there. The game makes no indication about this whatsoever (and if it does, it is very, very vague), and if you do not train those specific characters beforehand then you are pretty much screwed. I swear I facepalmed so hard when Sirius, a guy that I pretty much neglected throughout my playthrough, suddenly talk to my MU on the final map asking me to bring him, GAHHHHHHHH.
(I've never been that good with analogue I know, hahaha)