Lucina can do some work as a tank.
(Tank? Yes, tank)
Lucina sits at 29 defense, 40 hp and 36 speed, making her much better than Chrom with the similar "Paladin" build:
Weapon: Falchion (heals 10 every 3rd turn)
Support: Any will work. Ardent sacrifice / Reciprocal Aid makes her in to a healer as well (also combos with Defiant skills)
Special: Noon, Sol, Aether (to improve sustain)
Miracle (because we want to be annoying and undying).
A Skill: Distant counter (if you have too many Hectors) It helps with racking up special count if you are running aether.
Defiant Defense, Atk, Speed etc.
Fury (because you will heal so much any ways)
B Skill: Renewal 3 (because we like healing).
C Skill: Threaten Atk/Spd (once they are in range, you are even more tankier)
Threaten Defense if you want to be more aggressive.
P.S. Chrom fails with this build because his 29 top speed. He may have more bulk but he gets doubled by every one that matters (which makes him weaker, which is sad because he is not fulfilling his role as the tankiest of the 3).
But realistically, if you are tight on resources, I would say spend it on Azura because she is useful in PVP and can stab a red unit when you need it.