Ok so if you are on mobile, I figured out how to tame them with no violence. I put amarberries in my hotbar guessing that was like have them "out". Started following g this little guy around, and behold, his tame meter started rising!
Lystrosaurus:Easy Taming- Feed Mejoberries when ever it gets hungry.
-Speed:Pretty fast for its weight.
*Most Important for Beginners or others:If u tame a couple of these guys, U will have extra protection, they're big,strong, can keep up with u sometimes- they're very fast for their size and weight!*
1. Do not knock him out.
2. Feed him any berries, mejoberrys are more effective.
3. Don't let him get hungry for long time because the taming % will start dropping, so stay with him and wait until he get hungry again and feed him.
No need to knock out as it is a passive tame. Berries is best if a player does not have Rare Flowers. Easy tame, however, annoying because it will continue to walk around. Trapping it in a small area would best make it an easier tame and less wandering.
Once tamed, petting the Lystro will give experience boost to any dinos as well as players that are in its radius. I believe it lasts 5 minutes. So, when crafting a bunch of items, pet these little dogs.