If your entire world on the player side is squeezelite, IMHO there’s little to be gained using MA vs lyrion. I’m probably biased since I help maintain the Squeexebox HA integration though … I’ve looked at MA, but there’s just too many things in the Lyrion world - e.g. all the various radio plugins - that I’d miss too much.
In terms of your options, you’re always going to need an instance of LMS unless you use MA (which implements a cut down version of the protocol LMS uses). So, your option 1 is fine. Option 3 doesn’t exist - you integrate HA to LMS and LMS talks to your squeezelite players. You do have the option of installing LMS as an addon to HA (basically the same way that MA is intalled on HA). Home assistant community addons : LMS the Lyrion Music Server Formerly the Logitech Media Server or SqueezeBox Server. Squeezelite Player - Installation / Home Assistant OS - Home Assistant Community If you’re running HA anyway, that’s a nice route, but depends of course where your music library is stored.