This guide is written out of experience playing casual. Take caution when applying this to ranked. If you don't already know Lian's abilities, please visit the shooting range.
What the game or wiki won't tell you about Lian's kit is pre-fire and post-fire times of her abilities. I do not know them exactly but I estimate them to be the following:
Grace post-fire time: 0.45s
Valor post-fire time: 0.45s
The rest of her abilities (besides her ultimate) have pre-fire and post-fire times of 0s. I define pre-fire time as the delay before an ability activates (not to be confused with casting time). I define post-fire time as the delay after an ability has finished it's animation, during which time you are locked out of using abilities.
In my definitions, the following time stages happen when you use an ability: pre-fire time, casting time, animation time, post-fire time. The ability of your in-hand weapon activated by LMB or RT has a firing rate which does not count towards the time stages that I listed, it only happens in parallel.
Because grace and valor have post-fire times, they should be used at the end of a combo. Because Presence has a casting time of 0.5s, it should be used at the beginning of a combo.
Practice the following combos in the shooting range. Arrows indicate little to no delay in between abilities. Commas indicate a noticeable delay.
Heirloom Rifle -> Valor: 800 damage combo.
Heirloom Rifle -> Grace: 800 damage combo.
Presence -> Heirloom Rifle -> Valor: 1600 damage combo.
Presence -> Heirloom Rifle -> Grace: 1600 damage combo.
Presence -> Heirloom Rifle -> Valor, Heirloom Rifle -> Grace: 1600 damage combo followed by an 800 damage combo 0.45s later.
Presence -> Heirloom Rifle -> Grace, Heirloom Rifle ->Valor: 1600 damage combo followed by an 800 damage combo 0.45s later.
The order in which these abilities are sequenced is set up to minimize the total time it takes to achieve the total damage: that is, to maximize burst. Follow these combos for quick bursts of damage. If you simply use Lian's autoaim abilities whenever they are off cooldown, your damage will end up being fragmented due to the post-fire time delays.
Reducing cooldown of presence is very important in your loadout. Heraldry and Inheritance should both be in your loadout at levels no lower than a total of half your loadout points.
Hitting an enemy with Presence reduces its Cooldown by 5s.
Reduce your active Cooldowns by 40% after getting an Elimination.
Increase the travel distance of Grace by 15 units.
Increase your maximum Health by 50.
Increase your maximum Ammo by 1.
Presence should be your opening attack on all full health targets. Hitting 2 targets with presence at the same time resets it's cooldown. Getting a kill or assist at any time after hitting presence also resets it's cooldown. While Present Arms III sounds appealing for this loadout, Manifest Destiny III is better for closing down kills or retreating from threats.