Can I connect my LG tv to my HomePod mini

doubt it, without the aid of an appletv box

homepod does not work as bluetooth speakers

homepod can be airplay 2 played to but no tv's i ever heard about support transmitting airplay 2 the tvs that support airplay 2 (my lg tv does) only work as airplay 2 receivers

some people say if one connects the appletv box to the tv's ARC enabled hdmi port (if the tv have such a port)

you can read more about ARC here

HDMI - Wikipedia

It occurred to me that you may be able to use LG's iOS app for their "Smart" appliances to listen to your TV on an available iPhone or iPad, then redirect it to HomePods via AirPlay.

Curious, I opened the app for the first time in years. Sure enough, I managed to find the obscure switch, and I could hear TV audio on my iPhone (actually using connected AirPods). Sadly, the app seems to accomplish this TV audio with a hack that bypasses the normal iOS audio harness - when I looked at the AirPlay controls via Control Center to redirect the TV Audio I was hearing to the HomePods via AirPlay, I failed. The control thought I was still using the previous [now silent] app. App's flakey.

You might have better luck - I think the "LG ThinQ" app is too much of a hack to support this hack :-).