Bob: you are using Athletics to climb the tree so your DC is 10.Steve: you are using Untrained Improvisation and Climbing Lore, so your DC is only 5.
I think I see the confusion. Steve never uses Untrained Improvisation to do anything. He uses skill to do things, but when he’s untrained in those skills, he has a better-than-zero proficiency bonus because he has the Untrained Improvisation feet.
Also I’m not aware of Lore skills allowing one to use the Climb action, so Steve should probably use Athletics, which definitely allows one to use the Climb action. Fortunately for Steve, if he’s untrained in Athletics, he’ll get an increased proficiency bonus because he has Untrained Improvisation.
Uh, shouldn't the DC still be 10?
Yes, it should be 10, because the DC doesn’t vary on the basis of whether a character is trained. Just like a Dinosaur Lore check doesn’t vary depending on whether the PC making the check is trained.