still thinking if we really need this - I would suggest to use the connect and close events to keep track on the connection status. Example:

var lgtv = require("lgtv2")();
var tvConnected;
lgtv.on('close', function () {
    tvConnected = false;
});
lgtv.on('connect', function () {
    tvConnected = true;
});

That is true, the events could be also used for keeping track of the connection status, but i was thinking that it would be better to use the internal connection property since it is already anyway there and has the needed information to tell the current tv status.