Binary search - why it can be checked by lower bound

binary_search.cpp

bool binary_search(int arr[], int len, const int& key) {
    int l = 0, r = len - 1;
    while (l <= r) {
        int mid = (l + r) / 2;
        if (arr[mid] < key)
            l = mid + 1;
        else 
            r = mid - 1;
    }
    return a[l] == key;
}