Can I make the keyboard display lower case letters?

Sorry, no.

You can lock it in app caps by double tapping the shift button. ANd you just have to get used to knowing that you're defaulted to lower case unless you specify otherwise

It's really not that bad once you get used to it. Honestly the lack of an easy apostrophe bugged me more.

If you just can't get used to the on screen keyboard you may want to consider an external blue tooth keyboard. There are several keyboard/cases that turn your iPad into a near notebook

If you're still looking for the easy apostrophe hold the comma.

In my opinion, this is still one the silliest oversights in design by Apple. They can make the little switch button on flashlight icon in the control tray toggle between up and down, but they can't toggle the case of the letters to reflect the status of the Shift key? Seriously...without actually using your phone, can you tell me which icon represents Shift being enabled? Is it the black arrow with the white background or the white arrow with the grey background?

On the shift key a black arrow on a while background is upper case, white arrow on grey lower case. I believe the Swiftkey keyboard gives you upper and lower case letters on your keyboard.

There is an App that does it: it's called ShowCase, but it's not approved by Apple. I had it on my iPad till I updated to iOS 8.3 (which also killed my aviation GPS app, but that's a different problem).