That's a tough one. I've never actually had both cats and dogs, but I have birds and dogs. It's only natural of course for a dog's instinct to chase a smaller animal, especially if it runs! I have had my most tame bird, Dawn, around my dogs before. When I introduced them I had Tommy or Tasha sit and my hand on their collar, and then let them reach out and sniff a bit but not too close. The thing is my bird didn't take off so it was easier to control the situation, she was a little nervous of the dogs at first but not too bad unless they got close and then she'd peck their nose and the dog would back off.

When I had my Rainbow Bridge collie, Cody, the neighbor got a little kitten one day. The kitten just didn't seem to know to fear dogs too much, and soon learned she could bully Cody around by stalking him and pouncing out and startling him. He got to where he wanted nothing to do with her, but then again, she was a baby, and Cody was a collie which is a breed that especially has a tendency to be gentle to small creatures.

The only real suggestion I can think of at the moment is when they are in the same room to try to have a treat or toy on hand and try to distract Lady G from chasing the kitty. This gives her positive reinforcement too for leaving the kitty alone. I'd praise her like crazy if she breaks off chasing the cat to come check out what is going on with you too. If you were able to do something like this consistently I think she might start to lose interest in chasing the kitty.

Well, hopefully some of our people with both dogs and cats can offer some insight or advice too