Generally, guns are designed so that you can't touch the bullet before it's fired. She'd have to empower the bullet before loading it, hope it stayed empowered until she needed it — plus remembering to empower the full magazine of bullets before each patrol, and depower them afterwards.
An arbalest or crossbow will have the projectile mounted on top. She can probably touch it fairly easily with a finger or thumb to empower it appropriately for the current situation right before firing.
However, beyond that: a rifled gun works by forcing the bullet through the grooves in the barrel, which causes it to deform as it spins. Lily's power would just wreck the barrel — so, she'd have to be firing a smoothbore. And smoothbore guns usually have a fair amount of spread; it's a mechanical limitation of the design, meaning that a well-trained archer or crossbow-wielder is going to be more accurate. Her power might be able to negate some of the effects leading to that innate inaccuracy, but you'd have to offset that against the possibility of it just wrecking the wadding or patch (ruining the airtight seal necessary to properly accelerate the projectile, and resulting in misfires)
If you're firing power-enhanced super-projectiles, you generally want to minimise the chance of it going off in directions you don't desire.
And then, of course, there's the whole PR and "optics" thing of arming your underaged cadets with live weapons for patrols. Not so much an issue once she moves to the Protectorate, but certainly one while she's still a Ward.