Bookworm,
I’m sure you’re familiar with the fable of the girl/boy who cried wolf. Aesop I think? Anyway, you’ve built a wall up of lies with your parents & now you want that wall to disappear overnight.
I don’t think that’s fair or logical to ask of another person.
So I’m asking you to try to step back from your own situation & look at this logically; that it has nothing to do with you.
How many stories have you read about the one spouse that takes back the cheating spouse bec they said they’d never do it again.
Or the alcoholic who has a close call & says they’ll never drink again. Same with someone who has an addiction. They ask people to forgive them, make promises they can’t keep, lie & well.....when they really need something really important they end up alone.

Now I’m not saying your parents are going to leave or abandon you, no way, but the lying has created a distance between you guys.
Make sense?
So your job is to start to close that distance with being accountable. And I’d start out small.

Tell your parents something small...& then do it...& then tell them you kept your word. These will start to add up.
Like you tell them, “hey I’m going to run the vacuum in my room after school today,” (& if you’re my kid I’d think I had either heard you wrong or I had lost my mind lol), but then actually push yourself to do it...& then tell them you did it.
So this becomes a “habit.” You’re being accountable & after awhile you won’t need to tell them what you did; they will see it.

My dd lies just for the sake of lying & it’s become habitual for her. So there r lies that slide & lies that build up. But if you’re lying about everything, well what is there to believe? And why should anyone believe?
So maybe if it’s become a habit you’ll need to slow your conversation down in your head so your not lying. At least not lying as much. Lying has become a habit & habits are conditions in our psyche that we can change.
Children up to young adults use The amygdala part of their brain for making decisions. This is the emotional part of the brain bec your frontal cortex which contains reason is still growing. So you’re using quick emotions for answers. If you slow your emotions down, breathe, think & then react you’re changing how you view yourself & the situation.
Start small. Make small changes.
Best of luck!