Imagine that, his FE7 art has him with a book..
Lucius: The Light
Since healer builds don't tend to have a whole lot of variation, it's safe to say that Lucius is honestly a fairly typical healer, with some of his noteworthy qualities being his high Atk for a healer (tying with Elise and Lachesis and beat only by Genny), a high Res beaten only by Wrys letting him double as a Res tank if necessary, and the fact that he comes equipped with Pain+ and Miracle from the get-go, making him fairly economical to build. He also packs a higher Speed and HP than Genny, making his survivability against magic units substantially better than hers and establishing him as a good middle ground of tanking and attacking between Genny and Wrys in terms of staff infantry. All things said, his stats are optimized rather nicely, giving him a lot of utility.
Level 40 stats: HP: 34 / 37 / 41 Atk: 29 / 32 / 35 Spd: 26 / 30 / 33 Def: 10 / 13 / 17 Res: 32 / 35 / 38 Total: 146~148
Default skills: Weapon: Pain+ Assist: Martyr+ Special: Miracle Passive A: HP+5 Passive B: -- Passive C: --
Radiant Razer (AoE attacker + high-investment healer)
*Optimal Build* General Use, Arena Offense/Defense, Chain modes
Saintly Soul (AoE Attacker + budget healer)
General Use, Arena Offense, Chain modes
Brutal Bishop (high-investment attacker)
*High Investment* General Use, Arena Offense, Chain modes
Other Options:
Warding Stance and Distant Defense are powerful options for making Lucius into a strong Res tank, however, both are quite rare and high-budget skills, and it's normally more practical to simply boost Lucius' Attack in order to increase his healing efficacy anyway.
Breaker skills can offer him some degree of offensive or defensive specialization, keeping tome units from doubling him or allowing him to more easily kill speedy melee units like swords, but it's rarely worth using over staff-specific skills or even simply Wings of Mercy.
Updated 2/8/18 with offensive build, other options, and added mention of Wings of Mercy to budget healer build