How can I mirror my iPhone to an LG TV wirelessly?

are you sure your model support airplay 2 mirror? my lg tv does and it shows up in airplay displays when I click on that in control center along with my appletv box (though because I have the appletv box I very very rarely use the airplay 2 of the tv)

of cause you need to be on the same wifi network as the tv some wifi routers keep 2.4Ghz and 5Ghz as separate unbridged networks and if each are on each their wifi network it will not work (then one needs to make the router bridge the two networks in it's configuration)

and of cause if the iphone is not on wifi then it will not work across the internet

another thing to test is to pull the plug on the tv and the wifi router for a few secs and let them power up once again

First, check if your LG TV supports AirPlay by visiting this link: Home app - Accessories - Apple. If your TV doesn’t support AirPlay, you can use a mirroring app like DoCast, which works with many TV brands, including LG.