Don't attack it unless u have a plan a good one is to wait for it to land, throw a normal bola at it, then shoot tranq arrows at its head until it passes out, then feed it mejoberries or any type of berries, you may want to build a house around it to protect you and the lymantria from storms
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.