You can loop backward:

const aLastIndexOf = (str, ch) => {
    for (let index = str.length - 1; index >= 0; index--) {
        if (str[index] == ch)
            return index;
    }
    return -1;
}

An example:

const aLastIndexOf = (str, ch) => {
    for (let index = str.length - 1; index >= 0; index--) {
        if (str[index] == ch)
            return index;
    }
    return -1;
}

console.log(aLastIndexOf("hello", 'h'));
console.log(aLastIndexOf("hello", 'l'));
console.log(aLastIndexOf("hello", 'e'));

Personally, I wouldn't choose either solution. Here is why:

LastIndexOf:

The problem lies in the comparing of elements while searching through the array. It does compare the elements using strict equality. Therefore comparing objects will always fail, except they are the same. In OP case they are different.

Slice & reverse one-liner @adeneo

Given an array of three elements [{key: A},{key: B},{key: C}] and the lookup for the last index of key = D will give you an index of 3. This is wrong as the last index should be -1 (Not found)

Looping through the array

While this is not necessarily wrong, looping through the whole array to find the element isn't the most concise way to do it. It's efficient yes, but readability can suffer from it. If I had to choose one, I'd probably choose this one. If readability / simplicity is your friend, then below is yet one more solution.

A simple solution

We can make lastIndexOf work, we just need to make the value comparable (strict equality conform). Or simply put: we need to map the objects to a single property that we want to find the last index of using javascript's native implementation.

const arr = [ { key: "a" }, { key: "b" }, { key: "c" }, { key: "e" }, { key: "e" }, { key: "f" } ];

arr.map(el => el.key).lastIndexOf("e"); //4
arr.map(el => el.key).lastIndexOf("d"); //-1

// Better:
const arrKeys = arr.map(el => el.key);
arrKeys.lastIndexOf("c"); //2
arrKeys.lastIndexOf("b"); //1

A fast solution

Simple backwards lookup (as concise and as fast as possible). Note the -1 return instead of null/undefined.

const arr = [ { key: "a" }, { key: "b" }, { key: "c" }, { key: "e" }, { key: "e" }, { key: "f" } ];

const lastIndexOf = (array, key) => {
  for(let i = array.length - 1; i >= 0; i--){
    if(array[i].key === key)
      return i;
  }
  return -1;
};

lastIndexOf(arr, "e"); //4
lastIndexOf(arr, "x"); //-1