Luigi and Lucina are seen developing a slow but steady friendship: even if bumping in terms that might have driven each other aside. Luigi isn't too fond of swordswoman's formality and stoic demeanor, but can relate to her when coming to pessimism and cynical/negative outlook on many things. He also looks up to Lucina with huge respect and not only wishes, but works on being a strong and unwinded person like her.
Lucina again, finds Luigi pretty cowardly and uncapable of taking in negative feedback and more importantly, hardships towards himself dignifiedly- but she appreciates green understudy's big heart and devotion to his loved ones, and is easily entertained, even fascinated by Luigi's quirky and eccentric way of doing certain things.
Both can be seen together sometimes, whether it's Lucina trying to teach Luigi her self-taught determination and tenacity on fighting, while Luigi provides her his instinctual comfort through little joys or help, and might remind her when she worries or works too hard before Smash Fights. Still, both things have tendency to fail because each other's flaws, either Lucina's stubborness
if being worried for and Luigi's clumsiness or soft heart, but as said above, slow and steady.
