Sounds like submissive peeing. I echo what Brent/Steve said above.. try to desensitize the dog to having the leash taken on and off. It may be an association with the leash itself, or with the action of putting it on. You can leave a lead on the dog, long enough that you can grab it and lead him outside without triggering the behavior, and praise and reward whenever he makes it past the normal pee-spot (or as soon as you get outside if there isn't a specific location where the peeing normally occurs), and again for peeing in the correct place.
Submissive peeing is a appeasement gesture - he does it because he thinks that's what you want him to do. Since he's so little, chances are that leaning over him to put the leash on looks a little aggressive to him, and he's trying to tell you he doesn't want a fight. Then he pees, and you stand up, no longer leaning over him, so he thinks it's working. In order to get him to stop, you'll have to change how the routine appears to him. After having him on lead all the time long enough for him to consistently pee in the correct place, you can try to desensitize him to the action of putting the leash on to go out. If you offer him a treat to nibble while you latch on the leash, it might help. It may also help to have him jump up on a chair or somewhere he can be a little higher, and you don't have to approach him from above. Or have him get in your lap and clip it on him while he's cuddling there. Do whatever you can to show you aren't threatening him when you come with the leash. Changing leashes may also help him break the association between leashing up and peeing. I used to use a soft slip-lead leash with my smaller dog who was fearful of being handled, and taught her to "leash on" by putting her own head through the loop so she had more control over the situation.
He cowers when you approach with the leash? Try picking him up THEN attaching the leash.
Hey Kristen, did you manage to fix the problem? I'm facing exactly the same problem