This is the year that I am determined to get those perfect jumping lamb photos. I have posted some others here and in other posts. I welcome any advice from you photographers out there. My lens info is at the end of this post. 
Too darn many lambs in the way.
The lambs are most active in the evening when there is lower light. I am shooting with a larger aperture and therefore more shallow depth of field. Notice the lamb in focus is not the one that is jumping. In addition, those black lambs are hard to photograph in detail.
More lambs in the way. 
Lambs in the way AND depth of field issues.
Same problems.
And more lambs in the way.
Focal length issues again.
Lambs facing the wrong way.
Focal length and shutter speed issues.
I think I got this one on depth of field. Too bad the lamb is facing the wrong way.
Sort of OK but needs a faster shutter speed to really get it. Also the black one lying down is distracting.
This photo probably has the fewest issues.
The running lamb photos have similar challenges. These photos were all taken with my Nikon 40 mm f 2/8 lens to take advantage of the larger aperture but that gives me the more shallow depth of field. My other lens is the 18-135 mm f/3.5-5.6. Any recommendations?
Meridian Jacobs' Blog 
Great pictures! The made me laugh and smile. Your lambs are so adorable!
What if you got down low and show upward with the sky as your background? You would end up with a flying lamb against a bright blue sky. However you will need to make sure that you are either facing the camera north or south– aiming the camera east or west will causes unwanted shadows/glare.
In some areas of the pasture I have a better option for at least just having a green grass background. I can’t get much lower than in some of those photos because of where the lambs are. Hmmm. Once I put them in the other pasture there is a ditch that I could get in…but I might be waiting a long time for lambs to come by.
I cannot help with the technical issues. These pictures have filled me with joy!
I love these photos, especially the one with “the fewest issues” that looks like it is going boing, boing, boing. My photography method is take 100 and 10 will be good. The ones on the pasture seem to come out better than the ones in the shadow of the barn. Another issue is when the flash that lights up their eyes. ;-( What do we do about that??
That’s why I’m taking the photos with shutter speed priority to avoid using the flash. But then I don’t get photos in some areas (the barn for instance) because there is not enough light.
When working with fast moving erratic objects – which pretty much sums up lambs I reckon – then taking lots is the best option. I’d stick with the prime lens option, as it is one less variable to worry about. You can always push the ISO up – to 200/400 to give you more light to play with which should mean you can get away with using an aperture around the f/4 mark. Which should give you a bit more focal length.
That said, there is still a large amount of luck involved as the ability to coordinate a jumping lamb in front of its friends, facing in the right direction is well beyond my capacity 🙂
Yes, I think there is luck involved. Thanks for the comment. And thank goodness for digital so you can take hundreds of photos and hope you get lucky!