For an easy tame, wait for the Lymantria to land and then place a tent directly where he/she is at. Its stuck until the tents durability dies out, this gives you enough to build a little house around it for a safe, easy tame.
Get one wood foundation, ceiling, three walls, and one door frame that is NOT a double door way and a rare flower and bola. First you must locate one then place the foundation, then you must clear the area of all other creatures except the lymantria, then eat the rare flower and get its Agro, quickly get it over the foundation and bola it, then place the walls, door frame, and ceiling, then knock it out in anyway you see fit to you and feed it and you will have a flyer to get you a better flyer like and argy. Hope this helps
The Lymantria is like the Pteranodon on The Island, but it takes way more torpor then the Pteranodon. So easy taming is bola them (or wait until its landing) and place a tent on it ( DONT place the door of the tent in line to the head of the moth! It can really easy escape then. I hope I helped some of u Guys. Sry for my bad English btw.
If you cannot make a tent you can bola it, then place a wooden pillar basically in the middle of it. Then you put a thatch roof on the pillar and surround it by thatch door frames. It will be trapped and you can shoot it without it getting away.