If you want to achieve 100% privacy, you can't because when you want to send your on chain BTC to lightning wallet, you're leave a trace about it.
the quickest solution to mixing is what the chipmixer did by splitting the bitcoins into fixed inputs and giving the users a private key with an unknown time difference between the input and withdrawal addresses, this requires the mixer to contain a good amount of bitcoin, which I do not know why other mixers do not provide it.
Check whirlwind, their service work similar like what Chipmixer did. They also have a mining campaign that would stop after 10,000 deposits, this obviously they want to get a lot Bitcoin and increase the privacy level of their service.
It is not as good as a mixer but it can be used to make people lose track of you in some cases.
Yeah, as long as you didn't withdraw all of your deposited money in once.