Those capillaries will grow - know that your poking is helping that to happen and it will get easier. Hang in there!
Are you adding water to Lulu's canned food? That's one way to get fluid into a kitty and help them stay hydrated. Dehydrated kitties can also be hard to get blood from, although probably your issue is just that there aren't capillaries there yet.
How's Lulu behaving? She doing ok?