My LC is a 2009, so no apps, but on my 2020 Tundra, the remote start works via the "Toyota" app. I believe Entune is the legacy app and no longer supported. Edit: You will likely also need the "Remote Connect" subscription for that function...
Looked into this a bit more, didn't see a Toyota option but there is a LX 2 Row carpet mat in black PT206-60180-20 and Ivory PT206-60180-00 . Both around $95 online.