Lyman Ward is one of the most cantankerous dudes we've ever met, but even he has a soft spot for Ed and Ada Hawkes. Lyman has known Ada's family since he was a wee lad, and, in many ways, she provides him with a connection to that seemingly distant past.
Even their family histories are intertwined: Ada's father and grandfather worked for Lyman's father and grandfather. That's a big deal for Lyman. First, it means that she has a connection to all of those things he worries have been forgotten, like his granddad's Zodiac Mine. But, it's also something deeper: it establishes that Ada is on a lower social rung than he is. That's kind of a gross thing to say, but we do feel like Lyman likes Ada mostly because she serves him.
Despite this, Lyman certainly empathizes with Ada and her husband. After all, the three of them are so old that they're practically paleolithic—Lyman even admits that he worries sometimes about Ada's health. In his dream, Lyman imagines Ada suffering "some sort of seizure" and Ed "taking her in to the hospital" (9.1.130). On some level, this shows that Lyman genuinely worries about Ada's well-being.
So, how exactly does Lyman look at Ed and Ada? It's hard to say for certain, but we'd argue that the mere fact that this grumpy schmohawk allows them to be a part of his life shows that he holds them in some amount of esteem. Trust us on this one: that's saying a lot when you're talking about Lyman Ward.