How to watch Apple TV+ shows on a TV without the Apple TV device?
You can watch Apple TV+ on the web at tv.apple.com. From there, you can cast it to your Chromecast to watch on the LG tv.
LG has a few tv's that currently support Apple TV+ but there's only 4 of them right now and you need to use AirPlay 2 to send the content to the tv:
- LG OLED (2019)
- LG NanoCell SM8X series (2019)
- LG NanoCell SM9X series (2019)
- LG UHD UM7X series (2019)
As more manufacturers see if this is a success or not, you can expect to see changes in support.
I would recommend signing-up for the 7-day free trial and use a web browser to cast it to your tv. You can then decide if it's worth buying an inexpensive/used Apple TV 3rd gen to continue (or not if you don't mind using the Chromecast).
For more info on devices and shows you can visit Apple's overview page.