You're definitely going to want to use, bola, and tranq darts on this one. Too many arrows, will kill it outright(I'm not saying you can't use arrows. You have a high mortality rate if you put more than 3-4 arrows into it), very fragile tame. Bola it about a trikes length away from yourself initially... It's spore, is annoying to deal with.
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.
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.
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.
I tamed the lymantria in early game valguero and it was actually quite easy. All you need to do is use a bola (I used a normal one) and then keep attacking it with a club and it should get knocked out in couple of hits. However, if your trying to tame a higher level one, bring multiple bolas. The saddle is quite cheap so it can be utilised early game.