Elyra sits next to 4 phonetic neighbors — Lyra, Elvira, and Elira are the closest matches by sound. Most share Elyra's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"from Elysium, heavenly"
"rose, beauty"
"from the Eure river region"
"God is gracious, divinely gifted"
"lake, waterfall (from Welsh -lynn component)"
"one who achieves, one who attains her goals"
"light, bright"
"snow"
"Modern invented name; possibly a creative variant of Alexis (defend..."
"invented name combining La- (the) with -viah (echoing Hebrew -iah, ..."
"broad settlement with waterfall"
"creative act, the act of bringing into being"
"Her Majesty — a royal title indicating supreme authority and dignity"
"I believe"
Similar sound: These names share phonetic patterns with Elyra — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Greek origins, giving them the same cultural heritage as Elyra.
Rhythm: Elyra is a 3-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.