Just curious where the "wasabi is working with chain analysis" is coming from?
Their official announcements, where they said they hire a blockchain analysis company or companies, share data with them, spy on their users, and censor/blacklist users when they don't like what they find.
Which coinjoin would you recommend or would you recommend something else?
JoinMarket would be my first choice. You must run your own node for this. I would consider using Samourai/Whirlpool, but again, only via my own node. Alternatively, use ChipMixer.
What process would you recommend to gain privacy using LN?
The same as you would use for on-chain privacy. Buy coins anonymously, mix/coinjoin them for good measure, and then uses these anonymous coins to open a Lightning channel via my own node.
If you want further privacy, use it through Tor with no JavaScript.
It is
only possible to use via Tor. If you are on a clearnet ChipMixer site, you are being scammed.