Please post the definition from the lexicon or dictionary or the links you use so we can all have a look.
The word for grace in Ephesians 2:8 means this:
G5485 charis
Strong's Concordance
charis: grace, kindness
Original Word: χάρις, ιτος, ἡ
Part of Speech: Noun, Feminine
Transliteration: charis
Phonetic Spelling: (khar'-ece)
Definition: grace, kindness
Usage: (a) grace, as a gift or blessing brought to man by Jesus Christ, (b) favor, (c) gratitude, thanks, (d) a favor, kindness.
So there's nothing about grace being unmerited there. It doesn't exist in the context and the fact that one can fall from grace is further proof that grace isn't unmerited.
Galatians 5
4You who are trying to be justified by the law have been alienated from Christ; you have fallen away from grace.
So just using Galatians 5:4 as an example, there is a condition attached to grace, meaning there is something you and I can do to actually not be in God's grace. That's merited grace.
There's more examples, but that's one.
English dictionaries also define grace as favor, kindness, or goodwill with the leeway to make mistakes, keep the grace, with the expectation continual effort is being applied to stay in said grace.
In Christian theology, grace can mean "unmerited favor" but that's actually a denominational teaching rather than a Biblical teaching as I just showed you with Galatians 5:4.
So Christian theology isn't necessarily something explicitly Biblical. "Unmerited grace" is no exception.