Lymantrias typically are nonagressavive until attacked. Rather than a typical attack they use a large cloud of green acid that will temporarily slow your movement speed. The absolute best way of taming would be the bola method. To know our aim towards darts rather than the typical crossbow or stone and slingshot. Seeing as of these creatures have such low health. Happy taming!
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.
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.