Does it have to be injected into the left hand navigation? I'm not sure how to specifically do that, but here are 3 alternatives that I use frequently to accomplish the same business need and display the results on a page.
(1) Content Query Web Part (within one site collection), and point it at the target list
(2) Content Search Web Part (crossing site collections), and point it at the target list
(3) Another option otherwise is to use a Snippet web part and print the values on the screen using a real-time ajax request
$.ajax({
url : <REST/OData endpoint here pointing at your list>,
headers : "accept" : "application/json;odata=verbose",
success : function onSuccess(data, request){
// iterate returned values and print latest values here
},
error : function onError(error) {
// Error handling
}
});