If your question is asked of other customers then you may need to specify what LG television you are talking about.
You may wish to also contact the relevant LG help forum.
You may also wish to contact the Amazon help customer care team using the HELP or CONTACT US features on the Amazon website - this forum is Customer-to-customer so unless another customer has worked through your problem you may not get any assistance or support. :(
"Alexa" may not be what you are asking to connect to. Do you want to watch movies or something?
Not as such, Alexa is intended to be a voice operated system and your TV will not have a microphone. There may be an Alexa app available from the store supported by your TV but even if there is the Alexa app is not the full Alexa implementation as it is used to set up Alexa devices.
You could buy a fire stick or fire TV box and plug it into a spare HDMI socket both have a remote control which is voice activated (with a press button) using this would give you Alexa with some restrictions like no reminders etc but you can ask questions and get a voice reply, if for example you ask for the local weather you will get voice and also the info displayed on the TV.