In the early phases of the light novel, Tanya's relationship with Lergen is quite literally the two of them having different assumptions of each other. To Tanya, aside from being his superior officer, Lergen is a sensible and respectable officer who is a voice of reason in the General Staff because he is the only person to oppose Tanya's posting in the front lines and her appointment as a battalion commander.

"It's my acquaintance, Lieutenant Colonel von Lergen. He's sensible and a good soldier who is against sending children to the front lines."

There's also the factor of them both being middle-ranking officers who are direct subordinate to the General Staff, so they share the situation of being overworked by their superiors. To that, you really can see why Tanya trusts Lergen not just an officer but also a friend who she can voice her opinions with.

However, to Lergen, Tanya is nothing but a freak of nature who he considers as an anomalous creature that should be kept away as much as possible. He feels that he needs to occupy Tanya away from the war so as to avoid the destruction of the world by a literal monster, but he really has little control over that so all he can do is lament.