[X] Accept her offer. Whether or not you can trust what she says, she's left you a lot of room. If you can reduce the number of potential combatants, and perhaps evenavoid a fight entirely, you will.
[x] Wipe her off the map. She says she has power. You don't like the idea of a post-war Lystheni society having anybody entrenched, and a mid-war society with an obvious rallying point is just as undesirable.
[X] Refuse her offer. You are not acceding to restrictions on your actions when going into your army's first ground invasion. She can surrender in person to the soldiers who find her, just like everybody else.
[X] Shoot first, shoot often. Sucker punch the Lystheni with an all-out assault. You possess the advantage of quality. An alpha strike could easily burn half of the Lystheni's ships before they get their engines started, and secure the battle.