Chivo is a custodial lightning wallet (custodial bitcoin too). It literally says it is on the description.
Do people "use lightning" on Strike and Bitcoin Beach? Then yes, it is custodial lightning. You are getting semantic
Muun is not a true lightning wallet. But sure throw it in for fun.
Phoenix splicing upgrade is great improvement, but still not private, and still not trustless. You're not running your own node.
Yes, running your own node applies to on chain too, but the consequences for privacy are much less severe for Monero vs Lightning. The most a public Monero node could know is your IP. Not amounts, sender, or reciever. Not to mention the security implications for not having an active Lightning node that Monero doesn't have once txns are already confirmed.