If Lysithea has not previously been recruited, she can be seen in Chapter 14 “The Master Tactician” and be killed in the battle, but it is entirely possible to save her by the arrival of the Alymryan navy by defeating Claude. Byleth can still recruit her during the battle if they are the one to defeat her. Though she is badly wounded, Byleth can choose to either put her out of her misery or recruit her.
According to Fandom, Lysithea can be recruited even if you didn’t have her in your house.
