To add to that, your lawyer is bound by both professional, enforceable ethical guidelines as well as legal doctrine from revealing anything you've said to them in the course of their representation of you without your express consent. The number of exceptions to that is tiny. The only one that really matters is crime/fraud which relates not to your crime but using a lawyer to commit a crime. The others are either after you're dead (probate exception, where your lawyer can disclose information for the purposes of helping settle your will after your death) or are exclusively about money (your lawyer can disclose details of your agreed upon contract and payment structure if they are having to fight you to be paid).
There is zero reason to lie to your lawyer, all you do is make them less prepared in their defense.
No its not, holy shit.
Lying to your lawyer is a terrible idea. The lawyer is there to HELP YOU and present an effective defense. If you lie to the lawyer, the lawyer works with a different set of baseline arguments for your defense. If the lie is revealed, the defense is broken, it doesn't matter anymore. Months of work tossed out the window, nobody trusts the defendant anymore, and the lawyer needs to figure out damage control rather than actually defending you.
Repeat. If anyone finds out you lied, you are FUCKED. Trust goes out the window, Judge thinks you're a unrepentant idiot, most possibility of leniency in the case you are considered guilty is dropped.
It's literally one of the worst things you can do at trial.