Lao-ge is literally "old brother," and it's an affectionate but not overly intimate address. It's still not all that appropriate given the Envoy's status, but it's something you could comfortably call a colleague that you're friendly with. He never called the Envoy -ge without the Lao, but if he did use Heipao-ge it would feel a little more affectionate to me? Like on par with Bai Yu always calling Zhu Yilong, Long-ge.

-ge is a super common suffix used to call people from friends to boyfriends. And there are different modifiers to change the connotations, like Lao-ge. Or the colloquial shuài gē 帅哥 that sounds like you're calling a dude hot but turns out just to be a casual way of calling a man you don't know. And of course the much flirtier gege when used by an adult.

It's a pain to explain clearly in English! It's one of those "I know what it conveys when I hear it" things, haha.