You're given the choice to avoid her, but if you wish to recruit her you'll need to approach her and play along with her attempt to hypnotize you. Doing so will completely drain the Main Character's Mana. Eventually she notices that you're pretending and requests to join your party on your 5th meeting.
You can reject her however, which will land you in a battle against Lyra and her party of Light Spirits. It's a tough fight, but it will get you 5 uses of LightShards that gives +1 to Max Level and 1000 exp as well as full Health and Mana each. The LightShards are significant, as they work on the Main Character. They are extremely rare and cannot be crafted, so this is a great opportunity to get some.
Lyra is significant as she can summon Light Spirits, but unlike most summoners she can be recruited regardless of your chosen elemental affinity. This is important if you wish to evolve Celestials. The Light Spirits summoned by Lyra cost 10 stamina, which come small sized with an additional Floating trait. All of the Light Spirit's evolved forms already fly (with the exception of Light Nymphs), making the downside of Floating not worth it. Consider Lyra's Light Spirits a source of Floating to fuse to other units.