Mortimer Lightwood is an interesting cat. Even though the book spends a lot of time with him, he is one of the book's most invisible characters because he's so plain in his appearance and his mannerisms. Readers look at his buddy Eugene and think, "Oh yeah, the lazy jerk who falls in love and becomes a better man." But Mortimer is just plain vanilla from start to finish. The most recognizable thing about him is his dry sense of humor, which we see when he describes his work as a lawyer:
"I am one by myself, one," said Mortimer, "high up an awful staircase commanding a burial-ground, and I have a whole clerk to myself, and he has nothing to do but look at the burial-ground, and what he will turn out when arrived at maturity, I cannot conceive." (1.3.34)
Mortimer gives us some insight into his perspective on life when he agrees with his partner Eugene and says,
Precisely my view of the case, Eugene. But show me a good opportunity, show me something really worth being energetic about, and I'll show you energy. (1.3.36)
The fact is that both Mortimer and Eugene are lazy because they've never encountered anything in life that's worth getting excited about.
After Eugene's attempted murder by Bradley Headstone, Mortimer realizes just how much Eugene has always meant to him. Like Eugene, he snaps out of his lazy fog and decides that he'll put his life to good use—if only his best friend can survive. As he tells Eugene at his bedside,
You wanted to tell me something, Eugene. My poor dear fellow, you wanted to say something to your oldest friend—to the friend who has always loved you, admired you, imitated you, founded himself upon you, been nothing without you, and who God knows, would be here in your place if he could. (18.10.31)
The fact that Mortimer wants to trade places with Eugene shows that he has truly learned how to think selflessly, and this revelation has given him an entirely new (and better) outlook on life.