This is what somebody on serenaforest posted.
"Chrom's son. Undeniably it is head canon with support from fates. Some arguments (some Awakening evidence) is taken from Meteor's post. Credit to him. Without ado, lets find out why Lazward is Chrom's son. Some spoilers with supports.
1.Support with Marx
- Lazward: Master Marx, you don't have a Mark in your eye.
- Marx: Huh？A mark？
- Lazward: Yeah. Like, the crest of Nohr's royal family. I was wondering if you had that kind of mark.
- Marx: What in the world are you saying？ It would be painful if there was that sort of thing in your eye.
- Lazward: Ahhaha, you could say that, huh. But, the ruler of my country had it. So, I thought maybe Master Marx too...
- Marx: Huh… it's rare that you talk of your home.
Lazward says MY country. This means he is from Ylisse. Eligible Ylissean males for Olivia are Chrom, Frederick, Vaike, Stahl, Gaius, Libra, Kellam, Donnel and Ricken. 2. Class
Spoiler () Lazward users swords primarily. This leaves Chrom, Stahl and Gaius as possible daddies for our sword using unit.
3. Support with Soleil
- LAZWARD: Yeah. But, after I became your dad, I came to understand how my own mom and dad felt too. They wanted to protect their kid, even if it cost them their own life.
- SOLEIL: I... I don't want that!
- LAZWARD: I know. I won't die, I promise.
This talks about how Inigo doesn't wanna die and he wants to protect his daughter and how he will stay alive. This is parallel to Stahl's and Chrom's support from Future past. Both promise they will be alive.
- Inigo: All right, Father. But promise me you'll be okay. I couldn't stand to watch you die.
- Stahl: Neither one of us is going to die. I promise. We're going to be okay
- Inigo: ...... ...Yes. Thank you, Father.
- Chrom: No thanks needed. I wouldn't have it any other way.
- Inigo: Just promise you'll stay alive.
- Chrom: All right, I promise!
Gaius however, talks about Candy. We've narrowed it down to Stahl and Chrom. 3.Support with Flannel Spoiler ()
- Lazwald: I know what you're up to. I bet you came to show off some weird treasure?
- Flannel: As expected of Lazwald! Bingo!
- Lazwald: Ok, stop stop. Don't get too close to me.
- Flannel: What?! You can't see it if I don't come closer, right?
- Lazwald: Don't you remember? What happened the other day. You tried to show me this huuuuge weird bug... It flew right at my face and wouldn't get off.
- Flannel: Hahahahaha! That was hilarious!
- Lazwald: It was a disaster for me... it was so creepy. Anyways, I don't want to see something like that for a second time.
Where have we seen this before? The support between Inigo and Lucina as siblings. Inigo is afraid bugs in that support and is afraid in this one as well.
- Inigo: This place is a mess. I really should straighten up more...often... Is that a... AAAAAAAAAUGH!
- Lucina: Gods, I've never seen Inigo run so fast! Are we under attack?! Inigo! What happened back there? ...Are you all right?!
- Inigo: L-Lucinaaa!
- Lucina: Breathe, Inigo. Calm down and tell me what happened. You have nothing to fear now that I'm here.
- Inigo: B-b-bug! A bug!
- Lucina: ...A bug? ...As in...an insect?
- Inigo: As in a huge, horrid nightmare, with repulsive, hairy legs... It's TERRIBLE!
- Lucina: You're telling me all of your screaming and flailing was over an INSECT? *sigh* I thought the Risen had come. You could have sent the camp into a panic.
- Inigo: AAAAAH! It's back! And it can fly?! S-stay back! Don't come close, fiend!
Inigo being Chrom's son makes this support possible.
Meteor's: Olivia does not need to have any support conversations with Chrom to marry him. Thanks IS for forcing this pairing down my throat! Lucina, being a daddy's girl, knew knew all too well that Chrom would fall for her instantly, which is why she needed them to meet.
* Olivia and Inigo both wield swords. Chrom and Lucina also conveniently wield swords. incredible coincidence or family trait???
* Inigo looks fabulous in blue hair, just like in his official artwork.
* Lucina's support conversation with her mother is on the topic of dresses. Only Olivia wears dresses, so it's pretty safe to say this was written with her intended as the mother.
Expanding on some and my own
1.Expanding on the sword trait, look at the hero class. Now look at the Great Lord class. Both use swords and shields. Furthermore, the skill Sol, is half of the skill Aether which Chrom and Lucina have. This is representative of Inigo's inability to be like his dad. The hero class is also representative of him being similar to a great lord but not one. Also, the Falchion means more to Inigo then Lucina's other possible siblings. It is mentioned in his Lucina Sibling support and Chrom Future Past. Swords mean alot to this family.
You and she are...very alike.
Inigo is talking about how he's different, and how he can't be like Chrom and how Lucina is more like Chrom then he is.
2.Another reason why he is the son of Chrom is because they look alike. Inigo:
...We LOOK alike
IS is acknowledging that they look alike. Blue motiff for sword users (barring Owain) of the Royal family.
3.He has the brand. No other child that Chrom has(barring Lucina) has the brand. He is explicitly stated to have it. In his right eye to compliment Lucina's left. Inigo is the parallel to Lucina. They have similar traits but at the same time, he is the flamboyant, lucky go round compared to Lucina's seriousness.
Feel free to disagree and all. But the evidence is pretty overwhelming. Ahahah. The power of HEADCANON is staggering."
Now some of this stuff coming from the guy is more so red herring, but he does bring a excellent point with the bug fear that Inigo experiences a second time with the first being from his support with Lucina.
Now here's my stuff in reply.
It should also be taken into account that out of all the siblings for Lucina only Inigo and Morgan (they're the only siblings who can use swords) can potentially wield Falchion and if we're to go with Male Robin for a playthrough then that leads only Inigo as the potential sibling to Lucina because seriously Lucina's words don't make a lick of sense at all for the other non wielding swords users in the sibling supports to even bother using Falchion.
"If you are, in fact, among Falchion's chosen, that is knowledge we need. There may come a time when it proves necessary for you to take it up."
And there's no way I can see the other siblings making a cut that's split perfectly in two as Chrom said without some sort of experience and Marx was highly impressed by Lazward's swordplay when he first met him.