Can I screen mirror my iPad 2 to my lg tv

Yes - with the appropriate Apple adapter for your iPad and an HDMI cable - or via an AppleTV box using AirPlay.

If your iPad has a Lightning connector, you’ll need this:

Lightning Digital AV Adapter

https://store.apple.com/uk/xc/product/MD826ZM/A

If your iPad has a USB-C connector, you’ll need this:

USB-C Digital AV Multiport Adapter

https://store.apple.com/uk/xc/product/MUF82ZM/A

Or for AirPlay, either of these:

Apple TV HD

https://store.apple.com/uk/xc/product/MR912B/A//:0" height="314.5" width="316

Apple TV 4K

https://store.apple.com/uk/xc/product/MQD22B/A

You maybe able to use adapters and cables to physically mirror your iPad to your TV.

However, the older iOS version on that old, over 9-year old iPad 2 maybe too old a version and, therefore, too old a version of AirPlay to wirelessly AirPlay to much newer TV boxes.