When you start Owain's paralogue Lucina tells Lissa that she is still alive in the future and that she's an inspiration to others. Yet Owain has Lissa's ring and a piece of her staff as mementos. So is she alive in the future or not? --- To err is human. To blame your computer for your mistakes is even more human.
Actually, Owain's support is different with MU as a father than with other fathers. If MU is his father, he actually says he lost sight of MU in a battle against Risen, and never saw him again, and thus assumes he died.
Perhaps MU returned to the group for a while after he killed Chrom, masquerading as a good guy. Then, when he decided to leave, he left using a Risen attack as an excuse.
If that's the case Lucina would immediately suspect the MU not long after she arrived, as she would most likely want the news first from her father's best friend.
Most likely - MU separates from Owain in the chaos, MU catches a break and finds Chrom, Chrom and MU beat Validar and Grima takes over - Grima!MU vanishes to lead an army of Risen to destroy the world - and Yadda Yadda Yadda you know the story. --- I really never use signatures to be honest, but I figured I would put one here anyway.