Knocking out a high level lymantria within a single bola is impossible with a primitive crossbow. Instead, quickslot two pillars, two thatch ceilings, and five thatch walls. Bola the moth over flat land, then drop a pillar on one side. Ceilings next over it, then the other pillar on the other side. Hang walls from the ceilings. When it comes out of the bola, it's trapped. Tranq slowly so it won't die, and leave the trap up as a tame blind during taming. If you fail to trap it just try again; it won't flee far after a bola attack if you did no other attacks.
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.
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.
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.