You are no longer constrained by the Mimicry trait, but you may or may not be able to speak (depending on a DM ruling)
The introduction to lineages in Van Richten's Guide to Ravenloft state:
[...] If you choose a lineage, you might have once been a member of another race, but you aren't any longer. You now possess only your lineages racial traits.
The languages portion states:
If you are replacing your race with this lineage, you retain any languages you had and gain no new languages.
The Ancestral Legacy portion of the Hexblood Lineage states:
If you replace a race with this lineage, you can keep the following elements of that race: any skill proficiencies you gained from it and any climbing, flying or swimming speed you gained from it.
If you don't keep any of those elements or you choose this lineage at character creation, you gain two skills of your choice.
The Kenku race has the following relevant portion to combine with this:
Languages You can read and write Common and Auran, but you can speak only by using your Mimicry trait.
Taking all of these together we need to ask three questions:
- Is Mimicry a Racial Trait?
- Is Mimicry a Language?
- Can you speak as a result of your lineage?
Answering these questions will give us our answer.
Is Mimicry a Racial Trait?
Yes it is. As a result of the first rule for lineages quoted above, you no longer have the Mimicry racial trait. So you cannot use the Mimicry trait, but equally you are not constrained by it, provided there does not exist a more specific rule contradicting this rule.
Is Mimicry a Language?
The one rule we do have that might contradict this one, it is the one on languages, which states you retain any langauges from your race. So we must ask, is Mimicry a language, to which the answer is no.
It's not on the list of languages in the PHB or DMG.
It is not listed as a language in the Kenku's language section, but instead as (emphasis mine):
[...] your Mimicry trait.
Therefore, Mimicry is not a language, it is a racial trait, and by the rules of the lineage you do not have this trait anymore.
Can you speak as a result of your lineage?
Maybe. You can certainly read and write Common and Auran (as they are languages your race that you are replacing with the lineage specifically had). However it is silent on whether or not you can speak it (or indeed speak at all).
A DM could reasonably rule that you don't know how to speak (due to the loss of your Mimicry trait) and thus must learn to speak once more. Equally they could rule that the Mimicry trait is no longer restraining you from speaking normally, and since you know Common and Auran, you can speak them (though your accent and pronunciation may be off due to having lost your Mimicry trait).
What would I do as a DM?
If this DM were asked this, it would depend entirely on how recently the lineage had been applied in the character's backstory. If it were something that happened only very recently, then they would be able to understand other people speaking Common and/or Auran, but their speech would be odd, and they may default to trying to mimic another person's speech and find they cannot, or it sounds completely off. If on the otherhand this is something that character has had for a while, then they can absolutely speak normally with their own voice.