I think its quite disrespectful to your twins/children to give them such matchy names, Twins have enough trouble with separating themselves from their sibling without their parents treating them as if they are a singular entity. I feel like it's saying "you're not an individual" and is more interested in being cute than fostering an individual human's identity.
With that said I like
Lyra and
Myra although I wouldn't pronounce them to rhyme.
Some suggestions using
Lyra because I think it's the prettiest:
Lyra and
Moira Lyra and
Mira Lyra and
Marla Lyra and
RaynaLyra and
KaylaLyra and
ZaraLyra and
Maya - slant rhyme
Lyra and
KaraLyra and
Aria /
AryaLyra and
Talia