I've casted on grass for a long time, no issues. But yeah, I use a leader. You do not want to do it on concrete, that's harder on the line. Was the end of the line all fray'd up? You might be snapping it too quick, your pause between backcast and forward cast isn't long enough. With the leader, you'll hear a snap. That's the indication you were too quick on the forward stroke. With flies on, you snap flies off that way too.
Contrary to JackM's point, and this might be more dependent on skill level, but I prefer to give myself obstacles when practicing on lawns. The more practice can replicate reality, the better. And the reality is that I have obstacles on the stream. If I didn't, I probably wouldn't need to practice!
Also, the yarn trick to replicate the fly doesn't really work for me. It's too light, or grabs too much air, or something. It's just much more "floaty" than a real fly. I either go flyless, or else I cut the hook off of a fly at the bend.
Be careful when picking up the line, though, as Pete points out. Knots and the fly occasionally grab grass and weeds suddenly, it's easy to keep lifting. If it grabs the thicker portion of the leader, the rod can break before the line.
Dandelions are hell at grabbing stuff. But if there's just a few, they make nice targets.
