You have a ton of suggestions, but [name_f]Lyra[/name_f] and [name_f]Faye[/name_f] are such a fun pairing that I have to pile on 
Arya
[name_f]Cassia[/name_f]
[name_u]Eden[/name_u]
[name_f]Gwen[/name_f]
[name_f]Juno[/name_f]
[name_f]Maren[/name_f]
[name_f]Neve[/name_f]
Sybil was the first that came to mind, it would be a name for a sister to [name_f]Lyra[/name_f] and [name_f]Faye[/name_f] and [name_f]Sybil[/name_f] [name_u]Frost[/name_u] sounds very nice imo.
Some others ideas:
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Adele[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Agnes[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Alma[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Ayelet[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Beryl[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Bronte[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Bronwen[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Cecily[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Ceres[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Cleo[/name_f]/ [name_f]Clio[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Cybele[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Elspeth[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Elva[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Esme[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Ethel[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_u]Garnet[/name_u]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Gladys[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & Geneve/ [name_f]Geneva[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Gwyneth[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Harriet[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_u]Holly[/name_u]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Imogen[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Ines[/name_f]/ [name_f]Inez[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Ione[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Irene[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Isolde[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Juno[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Marilyn[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Melba[/name_f]/Melva
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Meryl[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Miriam[/name_f]/ [name_f]Miryam[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Myrtle[/name_f]/ [name_f]Myrta[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Nadine[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Nelda[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Neve[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Nerys[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Nimue[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Nona[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Noura[/name_f]/ [name_f]Nura[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Nydia[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Nyssa[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Odele[/name_f]/ [name_u]Odell[/name_u]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Olwen[/name_f]/ [name_f]Olwyn[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Olympe[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_u]Onyx[/name_u]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Oona[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Opal[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Orla[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Palma[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Pearl[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Poesy[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Quenby[/name_f]/ [name_u]Quinby[/name_u]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_u]Raven[/name_u]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Rhoswen[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_u]Risa[/name_u]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_u]Robin[/name_u]/ [name_f]Robyn[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Roxane[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_u]Ruby[/name_u]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Runa[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Ruth[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Sabine[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Selene[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Selma[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_u]Senna[/name_u]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_u]Simone[/name_u]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Sinead[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Soley[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Sonia[/name_f]/ [name_f]Sonya[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Susette[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Sylvie[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Tamsin[/name_f]/ [name_f]Tamsyn[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Tanis[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Taryn[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Thais[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Theda[/name_f]/ [name_f]Theta[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Toula[/name_f]/ [name_f]Tula[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Tova[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Twila[/name_f]/ [name_f]Twyla[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Winry[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Ylva[/name_f]/ [name_f]Ylfa[/name_f]
[name_f]Lyra[/name_f], [name_f]Faye[/name_f], & [name_f]Yvaine[/name_f]